An ideal gas at 27° C is compressed adiabatically to (8/27) of its original volume. If γ = 5/3, then the rise in temperature of a gas is (a) 300 K (b) 675 K (c) 375 K (d) 27 K

Answer: (c). T₂ = T₁((V₁)/(V₂))γ - 1 = 300(27/8)2/3 (27/8)2/3 = (3/2)² = 9/4, so T₂ = 675 K. Rise = 675 - 300 = 375 K So the answer is (c) 375 K.

An ideal gas at 27° C is compressed adiabatically to (8/27) of its… | MHT CET 2026 (16 Apr, Shift 1)

Q33MHT CET 2026 · 16 APR · SHIFT 1Medium

Thermodynamic Processes

An ideal gas at $27^\circ$ C is compressed adiabatically to $\left(\frac{8}{27}\right)$ of its original volume. If $\gamma = 5/3$ , then the rise in temperature of a gas is

Show answer and solution

Answer: (c)

$T_2 = T_1\left(\frac{V_1}{V_2}\right)^{\gamma - 1} = 300\left(\frac{27}{8}\right)^{2/3}$
$\left(\frac{27}{8}\right)^{2/3} = \left(\frac{3}{2}\right)^2 = \frac{9}{4}$ , so $T_2 = 675\text{ K}$ .
Rise $= 675 - 300 = 375\text{ K}$
So the answer is (c) 375 K.

Report a mistake

More questions on Thermodynamic Processes

An ideal gas is expanded adiabatically. How many times has the gas to be expanded to…MHT CET 2026 (15 Apr, Shift 2)
A monoatomic gas is stored in a thermally insulated container and the gas is suddenly…MHT CET 2026 (15 Apr, Shift 1)
A sample of gas at temperature T is adiabatically expanded to double its volume. The work…MHT CET 2026 (13 Apr, Shift 2)
An ideal gas expands adiabatically ( γ = 1.5). To reduce the r.m.s. velocity of the…MHT CET 2026 (13 Apr, Shift 1)
Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal…JEE Main 2026 (8 Apr, Shift 2)
The volume of an ideal gas increases 8 times and temperature becomes (1/4) th of initial…JEE Main 2026 (22 Jan, Shift 1)
An ideal gas having pressure P, volume V and temperature T is expanded isothermally, to a…MHT CET 2026 (20 Apr, Shift 2)
An ideal gas with pressure P, volume V and temperature T is expanded isothermally to…MHT CET 2026 (18 Apr, Shift 2)

Thermodynamic Processes question from MHT CET 2026 (16 Apr, Shift 1)

More questions on Thermodynamic Processes