The temperature of 1 mole of an ideal monoatomic gas is increased by 50 at constant pressure. The total heat added and change in internal energy are E₁ and E₂, respectively. If (E₁)/(E₂) = x/9 then the value of x is _________. Numerical answer type. Work it out, then open the answer.

Answer: 15. E₁ = nCpΔ T, E₂ = nCvΔ T, so (E₁)/(E₂) = γ. Monoatomic: γ = 5/3 = 15/9 So x = 15.

The temperature of 1 mole of an ideal monoatomic gas is increased by… | JEE Main 2025 (24 Jan, Shift 1)

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Thermodynamic Processes

The temperature of 1 mole of an ideal monoatomic gas is increased by $50^\circ\text{C}$ at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$ , respectively. If $\frac{E_1}{E_2} = \frac{x}{9}$ then the value of $x$ is _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 15

$E_1 = nC_p\Delta T$ , $E_2 = nC_v\Delta T$ , so $\frac{E_1}{E_2} = \gamma$ .
Monoatomic: $\gamma = \frac{5}{3} = \frac{15}{9}$
So $x = 15$ .

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