The temperature of 1 mole of an ideal monoatomic gas is increased by 50°C at constant pressure. The total heat added and change in internal energy are and , respectively. If then the value of x is ________. [2025]

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Solution

Q.
The temperature of 1 mole of an ideal monoatomic gas is increased by 50°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 ________. [2025]

Ans.
(15)

$△ T$ = 50°C = 50 K

n = 1 mole of ideal gas

$△ Q = n C_{P} △ T = E_{1}$

$△ U = n C_{V} △ T = E_{2}$

$\Rightarrow \frac{E_{1}}{E_{2}} = \frac{x}{9} = \frac{C_{P}}{C_{V}}$

For monoatomic gas $γ = \frac{C_{P}}{C_{V}} = \frac{5}{3}$

$\frac{x}{9} = \frac{5}{3} \Rightarrow x = 15$

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