The pressure of a monoatomic gas increases linearly from $4\times {10}^5$ N/m² to $8\times {10}^5$ N/m² when its volume increases from 0.2 m³ to 0.5 m³. Calculate  molar heat capacity of the gas [R = 8.31 J/mol k]  

1. 20.1 J/molK               

2. 17.14 J/molK

3. 18.14 J/molK                                   

20.14 J/molK

 

At ordinary temperatures, the molecules of a diatomic gas have only translational and rotational kinetic energies. At high temperatures, they may also have vibrational energy. As a result of this compared to lower temperatures, a diatomic gas at higher temperatures will have:

P-V diagram of a diatomic gas is straight line passing through origin. The molar heat capacity of the gas in the process will be

1. 4R

2. 2.5 R

3. 3R

4. $\frac{4\mathrm{R}}{3}$

If the temperature of source & sink in heat engine is
at 1000 K & 500 K respectively, then efficiency
can be
(1) 20%

(2) 30%

(3) 50%

(4) All of these

In an adiabatic process, work done versus change of
temperature $∆$T is

The volume and temperature graph is given in the figure below. If pressures for the two processes are different, then which one,  of the following, is true?

n moles of an ideal gas is heated at constant pressure
from 50°C to 100°C, the increase in internal energy
of the gas is $\left(\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}=\mathrm{\gamma }<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{R}=\mathrm{gas}<mspace\; width="1em"></mspace>\mathrm{constant}\right)$

1. $\frac{50<mspace\; width="1em"></mspace>\mathrm{nR}}{\mathrm{\gamma }-1}$

2. $\frac{100<mspace\; width="1em"></mspace>\mathrm{nR}}{\mathrm{\gamma }-1}$

3. $\frac{50<mspace\; width="1em"></mspace>\mathrm{n\gamma R}}{\mathrm{\gamma }-1}$

4. $\frac{25<mspace\; width="1em"></mspace>\mathrm{n\gamma R}}{\mathrm{\gamma }-1}$

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in the figure. The process of BC is adiabatic. The temperature at A, B and C are 400 K, 800 K, and 600 K respectively. Choose the correct statement:

1. The change in internal energy in the process AB is - 350R.

2. The change in internal energy in the process BC is - 500R.

3. The change in internal energy in the whole cyclic process is 250R.

4. The change in internal energy in the process CA is 700R. 

Which of the following shows the correct relationship between the pressure 'P' and density $\rho$ of an ideal gas at constant temperature?

(1) 

(2)

(3) 

(4)