Q: At constant pressure, density of a gas is :

Hint: Density of a substance is given by \rho = \dfrac{m}{V} , where m is the mass of the substance and V is its volume.Correction Option: BExplanation for correct option:By ideal gas equation: PV = nRT , where P , V , T and n are the pressure, volume, temperature and moles of the gas and R is the universal gas constant. \Rightarrow PV \alpha nRT \Rightarrow PV = \dfrac{m}{M} RT , where m and M are weight and molecular weight of the gas. \Rightarrow P = \dfrac{m}{V}\dfrac{{RT}}{M} Here, \rho = \dfrac{m}{V} and R' = \dfrac{R}{M} , where R' is the specific gas constant for the gas. \Rightarrow P = \rho R'T \Rightarrow \rho = \dfrac{P}{{R'T}} \therefore \rho \alpha \dfrac{1}{T} Hence, at constant pressure, density of a gas is inversely proportional to absolute temperature.

Question 1

A glass is full of water at  4^{0}C  when it is (a) cooled (b) heated. Then, which one of the following is correct?

Accepted Answer

When heated above  4^0 C, volume will increase, hence it will overflow.When cooled below  4^0 C, it also expands and  volume increases( anomalous expansion) until  0^0 C.Hence, in both cases it will overflow.

Question 2

The graph between temperature and pressure of a perfect gas is

Accepted Answer

From ideal gas equation, PV = nRTso P-T curve at constant volume is a straight line.If the temperature is written in Kelvin, it turns out that the intercept is at 273

Question 3

The graph drawn between pressure and temperature at constant volume for a given mass of different molecular weights  M_{1}  and  M_{2}  are the straight lines as shown in the figure then

Accepted Answer

From ideal gas equation, PV = nRT =  \frac{w}{M}RT Slope of P-T curve =  \frac{wR}{MV} Since V = constant and w = constant, we get that the slope is inversely proportional to molecular weightSteeper the line, more is slope, less is molecular weight.So,  M_{1} > M_{2}

Question 4

At constant pressure, density of a gas is :

Accepted Answer

Hint: Density of a substance is given by  ho  = \dfrac{m}{V}  , where  m is the mass of the substance and  V  is its volume.Correction Option: BExplanation for correct option:By ideal gas equation:  PV = nRT , where  P , V ,  T  and  n   are the pressure, volume, temperature and moles of the gas and  R  is the universal gas constant.  \Rightarrow PV \alpha  nRT  \Rightarrow PV = \dfrac{m}{M} RT , where  m  and  M  are weight and molecular weight of the gas.  \Rightarrow P = \dfrac{m}{V}\dfrac{{RT}}{M} Here,  ho  = \dfrac{m}{V}  and  R' = \dfrac{R}{M} ,  where  R'  is the specific gas constant for the gas.  \Rightarrow P = ho R'T  \Rightarrow ho  = \dfrac{P}{{R'T}} 	herefore ho  \alpha     \dfrac{1}{T} Hence, at constant pressure, density of a gas is inversely proportional to absolute temperature.

Question 5

All gasses deviate from gas laws at

Accepted Answer

At high pressure and low temperature, the molecular interaction terms become significant.So, we cannot neglect these terms.Also, the total size of molecules becomes significant at low temperatures.So, at low temperature and high pressure, there is a significant deviation from ideal gas equation.

Question 6

The temperature at which the volume of ideal gas is zero is:

Accepted Answer

From ideal gas equation,  PV = nRT This gives  V = \dfrac{nRT}{P} Now V tends to zero when T tends to zero where T is in KelvinSo, volume becomes 0 only when temperature =   0 K = -273 ^{\circ} C

Question 7

Two identical tumblers are filled fully with water at a certain temperature. One of the tumblers is warmed up and the other cooled down. But it is observed that the water overflows from both the tumblers. The temperature at which they are fully filled is

Accepted Answer

Water has anomalous expansion from  4^0 C( 277^0 K) to  0^0 C( 273^0 K). Water expands when heated from  4^0 C( 277^0 K) onwards.Since water overflows both the tumblers, the temp at which they are fully filled is  277^0 K

Question 8

If the slope of P-T graph for a given mass of a gas increases, then the volume of the gas

Accepted Answer

From ideal gas equation, PV = nRT =  \frac{w}{M}RT slope of P-T curve =  \frac{wR}{MV} since V = constant and w = constant, we get that the slope is inversely proportional to molecular weightSteeper the line, more is slope, less is volume.So as slope increases, volume decreases

Question 9

An ideal gas is that which

Accepted Answer

The concept of liquefaction of gases works on the principle of intermolecular forces of attraction between the gas molecules. Gases liquefy when these forces increase between the molecules, binding them together. But an ideal gas is one where the molecules do not influence each other, the explanation comes from Joule Thompson effect.

Question 10

The temperature at which a body does not radiate energy

Accepted Answer

Energy radiated becomes  0  only when absolute temperature becomes  0 .

Thermal Properties Of Matter

Physics
448 Views

A glass is full of water at $4^{0} C$ when it is (a) cooled (b) heated. Then, which one of the following is correct?

The graph between temperature and pressure of a perfect gas is

The graph drawn between pressure and temperature at constant volume for a given mass of different molecular weights $M_{1}$ and $M_{2}$ are the straight lines as shown in the figure then

At constant pressure, density of a gas is :

All gasses deviate from gas laws at

The temperature at which the volume of ideal gas is zero is:

Two identical tumblers are filled fully with water at a certain temperature. One of the tumblers is warmed up and the other cooled down. But it is observed that the water overflows from both the tumblers. The temperature at which they are fully filled is

If the slope of P-T graph for a given mass of a gas increases, then the volume of the gas

An ideal gas is that which

The temperature at which a body does not radiate energy

Thermal Properties Of Matter

Physics 448 Views

A glass is full of water at 40C when it is (a) cooled (b) heated. Then, which one of the following is correct?

The graph between temperature and pressure of a perfect gas is

The graph drawn between pressure and temperature at constant volume for a given mass of different molecular weights M1​ and M2​ are the straight lines as shown in the figure then

At constant pressure, density of a gas is :

All gasses deviate from gas laws at

The temperature at which the volume of ideal gas is zero is:

Two identical tumblers are filled fully with water at a certain temperature. One of the tumblers is warmed up and the other cooled down. But it is observed that the water overflows from both the tumblers. The temperature at which they are fully filled is

If the slope of P-T graph for a given mass of a gas increases, then the volume of the gas

An ideal gas is that which

The temperature at which a body does not radiate energy

Physics
448 Views

A glass is full of water at $4^{0} C$ when it is (a) cooled (b) heated. Then, which one of the following is correct?

The graph drawn between pressure and temperature at constant volume for a given mass of different molecular weights $M_{1}$ and $M_{2}$ are the straight lines as shown in the figure then