Relation Between Cp and Cv for an Ideal Gas

Author:H C Verma
JEE Main
IMPORTANT

Important Questions on Relation Between Cp and Cv for an Ideal Gas

HARD
IMPORTANT

An ideal gas having the density 1.7×10-3 g cm-3 at pressure 1.5×105 Pa is filled in a Kundt tube. When the gas is resonated at a frequency of 3.0 kHz, nodes are formed at a separation of 6.0 cm. Calculate the molar heat capacities CP and CV of the gas.

HARD
IMPORTANT

Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities CP and CV of the gas.

HARD
IMPORTANT

A mixture contains 1 mol of helium Cp=2.5R, CV=1.5R and 1 mol of hydrogen Cp=3.5R, CV=2.5R. Calculate the values of CpCV and γ for the mixture.

HARD
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Two ideal gases have the same value of CpCV=γ. What will be the value of this ratio for a mixture of the two gases in the ratio 1 : 2?

HARD
IMPORTANT

An ideal gas Cp/CV=γ is taken through a process in which the pressure and the volume vary as p=aVb. Find the value of b for which the specific heat capacity in the process is zero.

HARD
IMPORTANT

An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation p=kV. Show that the molar heat capacity of the gas for the process is given by C=CV+R2.

HARD
IMPORTANT

An amount Q of heat is added to a monatomic ideal gas in a process in which the gas performs a work Q2 on its surrounding. Find the molar heat capacity for the process.

HARD
IMPORTANT

An ideal gas expands from 100 cm3 to 200 cm3 at a constant pressure of 2.0×105 Pa when 50 J of heat is supplied to it. Calculate

(a) the change in internal energy of the gas.

(b) the number of moles in the gas if the initial temperature is 300 K.

(c) the molar heat capacity Cp at constant pressure.

(d) the molar heat capacity CV at constant volume.

HARD
IMPORTANT

A sample of air weighing 1.18g occupies 1.0×103cm3 when kept at 300 K and 1.0×105Pa. When 2.0cal of heat is added to it at constant volume, its temperature increases by 1 °C. Calculate the amount of heat needed to increase the temperature of air by 1 °C at constant pressure if the mechanical equivalent of heat is 4.2×107 erg cal-1. Assume that air behaves as an ideal gas.

MEDIUM
IMPORTANT

The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4calg1°C1 and 3.4  calg1°C1, respectively. The molecular weight of hydrogen is 2gmol1 and the gas constant R=8.3×107erg°C1mol1. Calculate the value of J.

HARD
IMPORTANT

A rigid container of negligible heat capacity contains one mole of an ideal gas. The temperature of the gas increases by 1°C if 3.0 cal of heat is added to it. The gas may be 

MEDIUM
IMPORTANT

The molar heat capacity for the process shown in figure  is

Question Image 

HARD
IMPORTANT

Figure shows a process on a gas in which pressure and volume both change. The molar heat capacity for this process is C.

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HARD
IMPORTANT

70 calories of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30 °C to 35 °C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is 

MEDIUM
IMPORTANT

Let CV and Cp denote the molar heat capacities of an ideal gas at constant volume and constant pressure respectively. Which of the following is a universal constant?

MEDIUM
IMPORTANT

The value of CPCV is 1.00 R for a gas sample in state A and is 1.08R in state B. Let pA, pB denote the pressure and TA and TB denote the temperatures of states A and B, respectively. Most likely

MEDIUM
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For a solid with a small expansion coefficient, 

EASY
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The ratio Cp/CV for a gas is 1.29. What is the degree of freedom of the molecules of this gas? 

HARD
IMPORTANT

In a real gas the internal energy depends on temperature and also on volume. The energy increases when the gas expands isothermally. Looking into the derivation of CpCV=R, find whether CpCV will be more than R, less than R or equal to R for a real gas.

EASY
IMPORTANT

Does a solid also have two kinds of molar heat capacities Cp and CV? If yes, do we have Cp>CV? Is CpCV=R?