Question

An insulated cylinder of volume \(60\,\text{cm}^3\) is filled with a gas at \(27^\circ\text{C}\) and \(2\) atmospheric pressure. The gas is then compressed making the final volume \(20\,\text{cm}^3\) while allowing the temperature to rise to \(77^\circ\text{C}\). The final pressure is ____________ atmospheric pressure.

Hint:

When both temperature and volume change, always use the combined gas law.

Answer 1

Correct Answer: 7

Step 1: Convert temperatures to Kelvin.
\[ T_1=27+273=300\,\text{K},\quad T_2=77+273=350\,\text{K} \]
Step 2: Apply combined gas law.
\[ \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2} \]
Step 3: Substitute given values.
\[ \frac{2\times60}{300}=\frac{P_2\times20}{350} \] \[ \Rightarrow P_2=\frac{2\times60\times350}{300\times20}=7 \]
Final Answer:
\[ \boxed{7} \]