JEE Advanced · 2006 · 09 Apr 2006 · Chemical Thermodynamics

WhatsApp Email

A monatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equals to 1. What is the molar heat capacity of the gas?

(A) $\frac{4 R}{2}$ ✓ Correct
(B) $\frac{3 R}{2}$
(C)5R/2
(D)0

Answer: (A)

Solution

For a process where

P / V = k

(constant), we have

P = k V

. Using the first law and the polytropic process relation, the molar heat capacity is

C = C_{V} + \frac{R}{1 - n}

, where

n

is the polytropic index. For

P V^{n} = constant

and

P = k V

, we get

n = - 1

. For a monatomic gas,

C_{V} = \frac{3 R}{2}

. Thus

C = \frac{3 R}{2} + \frac{R}{1 - ( - 1 )} = \frac{3 R}{2} + \frac{R}{2} = 2 R = \frac{4 R}{2}

JEE Advanced · 2006 · 09 Apr 2006 · Single correct option

Practise more: all JEE Advanced PYQs on Chemical Thermodynamics →

More JEE Advanced questions on Chemical Thermodynamics

An ideal gas (0.5 mol), initially at 2 bar pressure, is compressed at a constant temperature of 600 K in two steps : first against a constant external pressure of P bar $(2 < P < 8)$ , and then against constant external pressure of 8 bar. At each step, the compression is st …
JEE Advanced 2026View solution →
List-I contains various physical/chemical processes, and List-II contains combinations of changes in enthalpy $(Δ H)$ and entropy $(Δ S)$ . Match each entry in List-I to appropriate entry in List-II, and choose the correct option.

| List-I | | List …
JEE Advanced 2026View solution →
Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is ____.

Use: Universal gas constant $(R) = 8.3 J K^{- 1} mol^{- 1}$ ; Atomic mass (in amu): …
JEE Advanced 2025View solution →
Consider the following volume-temperature (V - T) diagram for the expansion of 5 moles of an ideal monoatomic gas.

(see diagram)

Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence …
JEE Advanced 2024View solution →
The entropy versus temperature plot for phases $α$ and $β$ at 1 bar pressure is given.
$S_{T}$ and $S_{0}$ are entropies of the phases at temperatures T and 0 K, respectively.

(see diagram)

The transition temperature for $α$ to …
JEE Advanced 2023View solution →
The entropy versus temperature plot for phases $α$ and $β$ at 1 bar pressure is given.
$S_{T}$ and $S_{0}$ are entropies of the phases at temperatures T and 0 K, respectively.

(see diagram)

The transition temperature for $α$ to …
JEE Advanced 2023View solution →