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 _______.

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answer is 15.

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Detailed Solution

Given that process is isobaric $ΔT = 50^{\circ} C$
Q in isobaric process $= {nC}_{P} ΔT = E_{1}$
$Δ$ U in isobaric process $= {nC}_{v} ΔT = E_{2}$
$∴ \frac{E_{1}}{E_{2}} = \frac{C_{P}}{C_{V}} = γ$
Given, gas is monoatomic
$\begin{aligned} ∴ γ & = 1 + \frac{2}{f} \\ = 1 + \frac{2}{3} \\ = \frac{5}{3} \end{aligned}$
Now, as per question.
$\begin{aligned} \frac{5}{3} = \frac{x}{9} \\ x = 15 \end{aligned}$