The temperature of 1 mole of an ideal monoatomic gas is increased by $$50^\circ C$$ 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  $$\underline{\hspace{2cm}}.$$

For 1 mole of an ideal monoatomic gas with temperature increase $$\Delta T = 50°C$$ at constant pressure:

Heat added at constant pressure: $$E_1 = nC_p\Delta T$$.

Change in internal energy: $$E_2 = nC_v\Delta T$$.

For a monoatomic ideal gas: $$C_p = \frac{5}{2}R$$ and $$C_v = \frac{3}{2}R$$.

$$\frac{E_1}{E_2} = \frac{C_p}{C_v} = \frac{5/2}{3/2} = \frac{5}{3}$$.

Given $$\frac{E_1}{E_2} = \frac{x}{9}$$:

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

$$x = 9 \times \frac{5}{3} = 15$$.

The answer is 15.