Thermodynamics - NEET Physics Questions
Question 11: moderate

A cylinder of capacity 20 litres is filled with H2 gas. The total average kinetic energy of translatory motion of its molecules is \( 1.5\times 10^{5}\) J. The pressure of hydrogen in the cylinder is

1. \[ 2\times 10^{6} N/m^{2}\]
2. \[ 3\times 10^{6} N/m^{2}\]
3. \[ 4\times 10^{6} N/m^{2}\]
4. \[ 5\times 10^{6} N/m^{2}\]
View Answer

The total average kinetic energy \( E \) of translatory motion for an ideal gas is given by:

\[
E = \frac{3}{2} nRT
\]

where:
- \( n \) is the number of moles,
- \( R \) is the gas constant (\( 8.314 \, \text{J/mol·K} \)),
- \( T \) is the temperature in Kelvin.

We can rearrange to find \( nRT \):

\[
nRT = \frac{2}{3} E
\]

The ideal gas law also gives us:

\[
PV = nRT
\]

Thus,

\[
P = \frac{nRT}{V} = \frac{\frac{2}{3} E}{V}
\]

Substitute \( E = 1.5 \times 10^5 \, \text{J} \) and \( V = 20 \, \text{litres} = 20 \times 10^{-3} \, \text{m}^3 \):

\[
P = \frac{\frac{2}{3} \times 1.5 \times 10^5}{20 \times 10^{-3}}
\]

\[
P = \frac{10^5}{20 \times 10^{-3}} = 5 \times 10^6 \, \text{N/m}^2
\]

So, the pressure is \( 5 \times 10^6 \, \text{N/m}^2 \).

Question 12: moderate

The amount of heat required to raise the temperature of 2 mole of monoatomic gas under isobaric condition from 0°C to 50°C will be :

1. 75 R
2. 125 R
3. 150 R
4. 250 R
View Answer

For a monoatomic gas under isobaric (constant pressure) conditions, the heat required \( Q \) is given by:

\[
Q = n C_p \Delta T
\]

where:
- \( n = 2 \) moles,
- \( C_p = \frac{5}{2} R \) (specific heat at constant pressure for monoatomic gas),
- \( \Delta T = 50^\circ \text{C} - 0^\circ \text{C} = 50 \) K.

Substitute values:

\[
Q = 2 \times \frac{5}{2} R \times 50 = 250R
\]

So, the answer is \( 250R \).

Question 13: moderate

Consider the following statements

A. Work and heat are path functions in thermodynamics.

B. The internal energy of a gaseous system is state function.

C. For gaseous system, CP is greater than CV .

D. Work done by gas at constant volume is zero.

Based on above information pick the correct option.

1. Only statement (A) is correct
2. Only statements (A), (B) and (C) are correct
3. Only statements (B), (C) and (A) are correct
4. All statements (A), (B), (C) and (D) are correct
View Answer

All the given statements are correct:

  • A. Work and heat depend on the path taken during a process, so they are path functions.
  • B. Internal energy depends only on the state of the system, making it a state function.
  • C. For gases,
    CP>CVC_P > C_V
     

    because extra heat is required at constant pressure to do expansion work.

  • D. At constant volume, the gas does no work since volume does not change (
    W=PΔV=0W = P\Delta V = 0
     

    ).