When a gas filled in a closed vessel is heated through `1^(@)C ` , its pressure is increased by 0.4 % . The initial temperature of the gas was

Options

A. `- 23^@ C`
B. `+23^@C`
C. `250^@ C`
D. `523^@C`

Answer

A

Explanation

Let `T_1 = T implies T_2 = (T + 1)`
And `p_1 = p implies p_2 = p + (0.4 p)/100 = (100.4)/(100) p`
From `(p_1V_1)/(T_1) xx (p_2V_2)/(T_2)`
`(pV)T = (100.4 o)/(100) xx V/((T + 1))`
`100 T + 100 = 100.4 T`
`0.4 T = 100`
`T = 100/0.4 = 250 K`
`= (250 - 273)^@C`
`= -23^@C`