Question

Given below are two statements
Statement-I: When μ amount of an ideal gas undergoes adiabatic change from state (P₁, V₁, T₁) to state (P₂, V₂, T₂), then work done is
\(W = \frac{μR(T2 - T1)}{1 - γ}\)
,where
\(γ = \frac{Cp}{Cv} \)and R = universal gas constant. 
Statement-II: In the above case, when work is done on the gas, the temperature of the gas would rise.
Choose the correct answer from the options given below.

• A. Both statement-I and statement-II are true
• B. Both statement-I and statement-II are false
• C. Statement-I is true but statement-II is false
• D. Statement-I is false but statement-II is true

Answer 1

The Correct Option is A

To determine the correctness of the given statements, let's examine each one in detail:

1. Statement-I: "When μ amount of an ideal gas undergoes an adiabatic change from state \((P_1, V_1, T_1)\) to state \((P_2, V_2, T_2)\), then work done is \( W = \frac{\mu R(T_2 - T_1)}{1 - \gamma} \), where \( \gamma = \frac{C_p}{C_v} \) and R is the universal gas constant."
   • An adiabatic process is one where no heat is exchanged with the surroundings. The work done during an adiabatic process for an ideal gas is given by: \( W = \frac{\mu R (T_2 - T_1)}{1 - \gamma} \).
   • This formula is derived from the first law of thermodynamics and is commonly used in thermodynamic processes for ideal gases.
   • Thus, Statement-I is true.
2. Statement-II: "In the above case, when work is done on the gas, the temperature of the gas would rise."
   • During an adiabatic compression (work done on the gas), the internal energy of the gas increases which results in an increase in temperature, as there is no heat exchange to balance this increase.
   • In thermal processes where work is done on the gas, the temperature of the gas increases if we assume no phase change or other heat exchange.
   • Therefore, Statement-II is also true.

Based on the above analysis, both statements are true, so the correct answer is:

Both statement-I and statement-II are true