Physics Q32 – JEE-MAIN 2025

Home Physics ThermodynamicsQuestion #525

Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from

T_{1}

T_{2}

is proportional to

(T_{2} - T_{1})

. Choose the correct answer from the options given below :

Clue 1 of 3: Adiabatic Process Definition

An adiabatic process is defined by no heat exchange with the surroundings, meaning $Q = 0$ .

🥷

Ninja Strategy•Elimination by fundamental properties

Quickly identify statements (A), (C), and (D) as false based on the fundamental definitions and relations of an adiabatic process, then eliminate options containing them.

🧠 Full Solution Path

Step 1: Analyze the characteristics of an adiabatic process✦ Active

An adiabatic process is defined by no heat exchange, so $Q = 0$ . According to the First Law of Thermodynamics, $Δ U = Q - W_{b y}$ , where $W_{b y}$ is work done by the system. Thus, for an adiabatic process, $Δ U = - W_{b y}$ . Alternatively, if $W_{o n}$ is work done on the system, then $Δ U = W_{o n}$ . For an ideal gas, internal energy $U$ depends only on temperature, so $Δ U = n C_{v} Δ T$ . For a monoatomic gas, $C_{v} = \frac{3}{2} R$ , so $Δ U = \frac{3}{2} n R (T_{2} - T_{1})$ . The adiabatic relations are $P V^{γ} = constant$ and $T V^{γ - 1} = constant$ , where $γ = \frac{C_{p}}{C_{v}} = \frac{5}{3}$ for a monoatomic gas.

Step 2: Evaluate each statement (A) to (E)○ Expand

(A) Internal energy is constant. False. In an adiabatic process, work is done, leading to a change in temperature and thus internal energy ( $Δ U \neq 0$ ). (B) Work done in the process is equal to the change in internal energy. True. If 'Work done' refers to work done *on* the system ( $W_{o n}$ ), then from the First Law ( $Δ U = Q + W_{o n}$ ) and $Q = 0$ , we get $Δ U = W_{o n}$ . (C) The product of temperature and volume is a constant. False. The correct relation is $T V^{γ - 1} = constant$ , not $T V = constant$ . (D) The product of pressure and volume is a constant. False. The correct relation is $P V^{γ} = constant$ , not $P V = constant$ (which is for an isothermal process). (E) The work done to change the temperature from $T_{1}$ to $T_{2}$ is proportional to $(T_{2} - T_{1})$ . True. Since $Δ U = \frac{3}{2} n R (T_{2} - T_{1})$ , and work done is directly related to $Δ U$ (either $W_{o n} = Δ U$ or $W_{b y} = - Δ U$ ), the work done is proportional to $(T_{2} - T_{1})$ .

💡 Teacher's Secret Hint

Pay close attention to the convention for work done in statement (B). The most common convention in this context makes (B) true.

Step 3: Identify the correct combination of statements○ Expand

Based on the evaluation, statements (B) and (E) are true, while (A), (C), and (D) are false. Therefore, the correct option is the one that includes only (B) and (E).

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Physics Question 32 – JEE-MAIN 2025

Clue 1 of 3: Adiabatic Process Definition

🧠 Full Solution Path