Question

A gas occupies a certain volume at 27 degree celcius.If it is heated at constant pressure, its volume is exactly doubled at a temperature o

Answer 1

Answer on Question#40067 – Physics – Molecular Physics | Thermodynamics

A gas occupies a certain volume at 27 degree celcius. If it is heated at constant pressure, its volume is exactly doubled at a temperature

Solution:

$\mathrm{T}_{1} = 300\mathrm{K}$ — initial temperature of a gas

We can use the combined gas equation $(P = const)$:

$$\frac{\mathrm{PV}_1}{\mathrm{T}_1} = \frac{\mathrm{PV}_2}{\mathrm{T}_2}$$ $$V_2 = 2 \cdot V_1$$

(2)in(1):

$$\frac{P_1 V_1}{T_1} = \frac{P_2 (2 \cdot V_1)}{T_2}$$ $$\frac{P_1 V_1}{T_1} = \frac{P_1 (2 \cdot V_1)}{T_2}$$ $$\frac{V_1}{T_1} = \frac{2 \cdot V_1}{T_2}$$ $$T_2 = 2 T_1 = 2 \cdot 300\mathrm{K} = 600\mathrm{K}$$

Answer: volume of the gas is exactly doubled at a temperature $600\mathrm{K}$.