Two moles of an ideal gas with \dfrac{C_P}{C_V}=\dfrac{5}{3} are mixed with 3 moles of another ideal gas with \dfrac{C_P}{C_V}=\dfrac{4}{3} . The value of \dfrac{C_P}{C_V} for the mixture is :

Let n_1,n_2 be the number of moles of gases 1 and 2 .We have \dfrac{C_{p_1}}{C_{v_1}}=\dfrac{5}{3} and We know C_{p_1}=C_{v_1}+R \therefore \dfrac{5C_{v_1}}{3}=C_{v_1}+R,\dfrac{2C_{v_1}}{3}R_1,C_{v_1}=\dfrac{3R}{2} A and C_{p_1}=C_{ v_ 1 }+R=\dfrac{5R}{2} Also, \dfrac{C_{ p_ 2}}{C_{ v_ 2 }}=\dfrac{4}{3} and C_{p_2}=C_{v_2}+R \therefore \dfrac{4C_{ v_ 2 }}{3}=C_{ v_ 2 }+R, \dfrac{C_{ v_ 2 }}{3}=R,C_{ v_ 2 }=3R C_{ p_ 2}=C_{ v_ 2 }+ R=4R Now C_{ v_ {mix} }=\dfrac{n_1C_{ v_ 1 }+n_2C_{ v_ 2 }}{n_1+n_2}=\dfrac{2\times \dfrac{3R}{2}+3\times 3R}{2+3} =\dfrac{3R+9R}{5}=\dfrac{12R}{5} C_{ p_ {mix} }=\dfrac{n_1C_{ p_ 1 }+n_2C_{ p_ 2 }}{n_1+n_2}=\dfrac{2\times \dfrac{5R}{2}+3\times 4R}{2+3} =\dfrac{17R}{5} l_{mix}=\dfrac{C_{ p_ {mix} }}{C_{ v_ {mix} }}=\dfrac{17}{12}=1.4166=1.42 Option (C) is correct.

A solid aluminium sphere and a solid lead sphere of the same radius are heated to the same temperature and allowed to cool under identical surrounding temperatures. The specific heat capacity of aluminium = 900\space J/kg^{0}C and that of the lead = 130 \space J/kg^{0}C . The density of lead = 10^{4} \space kg/m^{3} and that of aluminum = 2.7 \times 10^{3} \space kg/m^{3}\space kg/m^{3} . Assume that the emissivity of both thespheres is the same When the temperature of spheres T is not too different from the surrounding temperature, the radiating object obeys

Power radiated by an object to the surrounding temperature T_0 P = e \sigma A(T^{4} - T^{4}_0) = \sigma eA(T^{2} + T^{2}_0) (T_0 + T_0) (T - T_0) = 4e\sigma \space A \space T^{3}_0 \Delta T P \space \alpha \space \Delta T The net power radiated is approximately proportional to the temperature difference, in agreement with Newton's law of cooling it (T - T_0) is small.

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11th
Physics
Thermal Properties of Matter
Heat Capacity
$Heat Capacity Questions and...$

Important questions on Heat Capacity

Q: Equal heat is gives to two objects A and B of mass 1 g. Temperature of A increases by 3^oC and B by 5^oC . Which object has more specific heat? And by what factor?

Given that mass of A and B is equal and =1g=m_A=m_B Given change in temperature of A=\Delta T_A=3^0C change in tem. of B=\Delta T_B=5^0C Given that Equal amount of heat is applied to both for A:\,Q=m_{A}S_A\Delta T_A=3S_A ............(i)for B:\,Q=m_{B}S_B\Delta T_B=5S_B ............(ii)Where S_A and S_B are specific heat of A and B From eq (i), (ii) 3S_A=5S_B \Rightarrow \boxed{S_A=\dfrac{5}{3}S_B} Hence specific heat of A is greater than that of B by a factor of 5/3

Q: An engineer is developing an electric water heater to provide a continuous supply of hot water . One trial design is shown in Fig. 1B.14 . Water is flowing at the rate of 0.500 \,kg / min , the inlet thermometer registers 18.0^{\circ} C , the voltmeter reads 120 V , and the ammeter reads 15.0 A ( corresponding to a power input of ( 120 V ) (15.0 A ) = 1800 W ) . (a) When a steady state is finally reached , what is the reading of the outlet thermometer ? (b) Why is it unnecessary to take into account the heat capacity mc of the apparatus itself ?

B] It is unnecessary to take into account the heat capacity of apparatus because water takes heat from it also and in this way its temperature remains constant.

Q: An immersion heater, in an insulated vessel of negligible heat capacity, brings 100 g of water to the boiling point from 16^{0}C in 7 min. Then Power of heater is nearly

In 7 min , temperature of 100 g of water is raised by (1000 - 16^{0}C) = 84^{0}C . The amount of the heat provided by heater Q_W = C_Wm_W\Delta T = (1 cal/g^{0}C)(100 g)(84^{0}C) = 8.4 \times 10^{3} cal = (8.4 \times 10^{3} \times 4.186) J \simeq 3.5 \times 10^{4} J Power of heater = \frac {Q_W} {t_1} = \dfrac {8.4 \times 10^{3} cal} {(7 \times 60)_s} = 20 cal/s = (20 \times 4.18) J/s = 83.6 W = 84 W

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easy92 Questionsmedium132 Questionshard38 Questions

HARD

After the tea is added to the thermos, the temperature of the liquid quickly falls from $8 0^{o} C$ to $7 5^{o} C$ as $i$ reaches thermal equilibrium with the thermos flask
What is the heat capacity of the thermos?

$9.5 J / K$

$14 J / K$

$95 J / K$

$878 J / K$

View Answer

HARD

The value of $C_{p} - C_{v}$ is 1:00 R for a gas sample in state A and is 1.08 R in state B. Let $P_{A}, P_{a}$ denote the pressures and $T_{A} a n d T_{a}$ denote the temperature of the states $A$ and $a$ respectively.Most likely

$P_{A} < P_{a} a n d T_{A} > T_{e}$

$P_{A} > P_{a} a n d T_{A} < T_{a}$

$P_{A} = P_{a} a n d T_{A} < T_{a}$

$p_{A} > P_{a} a n d T_{A} = T_{e}$

View Answer

HARD

Equal heat is gives to two objects A and B of mass 1 g. Temperature of A increases by $3^{o} C$ and B by $5^{o} C$ . Which object has more specific heat? And by what factor?

View Answer

HARD

If, after some of the tea has been transferred to the thermos (as described in the passage), the teapot with its contents (at a temperature of $8 0^{o} C$ ) was placed or the insulated warmer for $5$ minutes, what would be the temperature at the end of this $5$ minutes period (Assume that no significant heat transfer occurs with the surrounding):

$80.7^{o} C$

$82.5^{o} C$

$83.2^{o} C$

$95.2^{o} C$

View Answer

HARD

Two moles of an ideal gas with $\frac{C _{P}}{C _{V}} = \frac{5}{3}$ are mixed with $3$ moles of another ideal gas with $\frac{C _{P}}{C _{V}} = \frac{4}{3}$ . The value of $\frac{C _{P}}{C _{V}}$ for the mixture is :

$1.47$

$1.45$

$1.42$

$1.50$

View Answer

HARD

What is the final temperature of the system ?

$4 8^{o} C$

$7 2^{o} C$

$9 4^{o} C$

$10 0^{o} C$

View Answer

HARD

An engineer is developing an electric water heater to provide a continuous supply of hot water . One trial design is shown in Fig. 1B.14 . Water is flowing at the rate of $0.500 k g / m i n$ , the inlet thermometer registers $18 . 0^{\circ} C$ , the voltmeter reads $120 V$ , and the ammeter reads $15.0 A$ ( corresponding to a power input of $(120 V) (15.0 A) = 1800 W$ ) . (a) When a steady state is finally reached , what is the reading of the outlet thermometer ? (b) Why is it unnecessary to take into account the heat capacity $m c$ of the apparatus itself ?

View Answer

HARD

An alternative method for keeping the tea hot would be to place the teapot on a $10$ pound block that has been heated in an oven to $30 0^{o} C$ . A block of which of the following substance would best be able to keep the tea hot?

copper (specific heat $= 0.39 J / g K$ )

granite (specific heat $= 0.79 J / g K$ )

iron (specific heat $= 0.45 J / g K$ )

pewter (specific heat $= 0.17 J / g K$ )

View Answer

HARD

An immersion heater, in an insulated vessel of negligible heat capacity, brings 100 g of water to the boiling point from $1 6^{0} C$ in 7 min. Then
Power of heater is nearly

$8.4 \times 1 0^{3}$

$84 W$

$8.4 \times 1 0^{3}$ cal/s

$20 W$

View Answer

HARD

A solid aluminium sphere and a solid lead sphere of the same radius are heated to the same temperature and allowed to cool under identical surrounding temperatures. The specific heat capacity of aluminium = $900 J / k g^{0} C$ and that of the lead = $130 J / k g^{0} C$ . The density of lead = $1 0^{4} k g / m^{3}$ and that of aluminum = $2.7 \times 1 0^{3} k g / m^{3} k g / m^{3}$ . Assume that the emissivity of both the
spheres is the same
When the temperature of spheres T is not too different from the surrounding temperature, the radiating object obeys

Important questions on Heat Capacity

After the tea is added to the thermos, the temperature of the liquid quickly falls from 80oC to 75oC as i reaches thermal equilibrium with the thermos flask What is the heat capacity of the thermos?

9.5 J/K

14 J/K

95 J/K

878 J/K

The value of Cp​−Cv​ is 1:00 R for a gas sample in state A and is 1.08 R in state B. Let PA​,Pa​ denote the pressures and TA​ and Ta​ denote the temperature of the states A and a respectively.Most likely

PA​<Pa​ and TA​>Te​

PA​>Pa​ and TA​<Ta​

PA​=Pa​ and TA​<Ta​

pA​>Pa​ and TA​=Te​

Equal heat is gives to two objects A and B of mass 1 g. Temperature of A increases by 3oC and B by 5oC. Which object has more specific heat? And by what factor?

80.7 oC

82.5 oC

83.2 oC

95.2 oC

Two moles of an ideal gas with CV​CP​​=35​ are mixed with 3 moles of another ideal gas with CV​CP​​=34​. The value of CV​CP​​ for the mixture is :

1.47

1.45

1.42

1.50

What is the final temperature of the system ?

48oC

72oC

94oC

100oC

An alternative method for keeping the tea hot would be to place the teapot on a 10 pound block that has been heated in an oven to 300oC. A block of which of the following substance would best be able to keep the tea hot?

copper (specific heat =0.39 J/g K)

granite (specific heat =0.79 J/g K)

iron (specific heat =0.45 J/g K)

pewter (specific heat =0.17 J/g K)

An immersion heater, in an insulated vessel of negligible heat capacity, brings 100 g of water to the boiling point from 160C in 7 min. Then Power of heater is nearly

8.4×103

84W

8.4×103 cal/s

20W

Stefan-Boltzmann law

Newton's law of cooling

Dulong-Petit law

Planck's law

More important questions

After the tea is added to the thermos, the temperature of the liquid quickly falls from $8 0^{o} C$ to $7 5^{o} C$ as $i$ reaches thermal equilibrium with the thermos flask
What is the heat capacity of the thermos?

$9.5 J / K$

$14 J / K$

$95 J / K$

$878 J / K$

The value of $C_{p} - C_{v}$ is 1:00 R for a gas sample in state A and is 1.08 R in state B. Let $P_{A}, P_{a}$ denote the pressures and $T_{A} a n d T_{a}$ denote the temperature of the states $A$ and $a$ respectively.Most likely

$P_{A} < P_{a} a n d T_{A} > T_{e}$

$P_{A} > P_{a} a n d T_{A} < T_{a}$

$P_{A} = P_{a} a n d T_{A} < T_{a}$

$p_{A} > P_{a} a n d T_{A} = T_{e}$

Equal heat is gives to two objects A and B of mass 1 g. Temperature of A increases by $3^{o} C$ and B by $5^{o} C$ . Which object has more specific heat? And by what factor?

$80.7^{o} C$

$82.5^{o} C$

$83.2^{o} C$

$95.2^{o} C$

Two moles of an ideal gas with $\frac{C _{P}}{C _{V}} = \frac{5}{3}$ are mixed with $3$ moles of another ideal gas with $\frac{C _{P}}{C _{V}} = \frac{4}{3}$ . The value of $\frac{C _{P}}{C _{V}}$ for the mixture is :

$1.47$

$1.45$

$1.42$

$1.50$

$4 8^{o} C$

$7 2^{o} C$

$9 4^{o} C$

$10 0^{o} C$

An alternative method for keeping the tea hot would be to place the teapot on a $10$ pound block that has been heated in an oven to $30 0^{o} C$ . A block of which of the following substance would best be able to keep the tea hot?

copper (specific heat $= 0.39 J / g K$ )

granite (specific heat $= 0.79 J / g K$ )

iron (specific heat $= 0.45 J / g K$ )

pewter (specific heat $= 0.17 J / g K$ )

An immersion heater, in an insulated vessel of negligible heat capacity, brings 100 g of water to the boiling point from $1 6^{0} C$ in 7 min. Then
Power of heater is nearly

$8.4 \times 1 0^{3}$

$84 W$

$8.4 \times 1 0^{3}$ cal/s

$20 W$