A gas at 27°C has a volume V and pressure P. On heating its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be

Correct Option: 1527°C

Step-by-step Explanation:

To find the resulting temperature of the gas, we can use the combined gas law, which relates the pressure, volume, and temperature of a fixed amount of gas:

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

where:
- $P_1$ and $P_2$ are the initial and final pressures,
- $V_1$ and $V_2$ are the initial and final volumes, and
- $T_1$ and $T_2$ are the initial and final absolute temperatures in Kelvin.

Step 1: Convert the initial temperature to Kelvin
The initial temperature is given in Celsius: 27°C. To convert it to Kelvin, we add 273:

$T_1=27+273=300\text{K}$

Step 2: Identify initial and final conditions
From the given information:
- Initial pressure, $P_1=P$
- Initial volume, $V_1=V$
- Final pressure, $P_2=2P$ (since pressure is doubled)
- Final volume, $V_2=3V$ (since volume becomes three times)

Step 3: Substitute the values into the gas law equation

$\frac{P\times V}{300}=\frac{\left(2P\right)\times \left(3V\right)}{T_2}$

Simplifying the right side of the equation:

$\frac{PV}{300}=\frac{6PV}{T_2}$

Divide both sides by $PV$:

$\frac{1}{300}=\frac{6}{T_2}$

Cross-multiplying to solve for $T_2$:

$T_2=6\times 300=1800\text{K}$

Step 4: Convert the final temperature back to Celsius
To express the resulting temperature in Celsius, we subtract 273 from the Kelvin temperature:

$T_2(°\text{C})=1800-273=1527°\text{C}$

Therefore, the resulting temperature of the gas will be 1527°C.