MHT CET · Chemistry · Thermodynamics (C)
The pressure of a gas is \(100 \mathrm{kPa}\). If it is compressed from \(1 \mathrm{~m}^{3}\) to \(10 \mathrm{dm}^{3}\), find the work done.
- A \(990 \mathrm{~J}\)
- B \(9990 \mathrm{~J}\)
- C \(9900 \mathrm{~J}\)
- D \(99000 \mathrm{~J}\)
Answer & Solution
Correct Answer
(D) \(99000 \mathrm{~J}\)
Step-by-step Solution
Detailed explanation
Given,
\(
\text {pressure, } p=100 \mathrm{kPa}=10^{5} \mathrm{~Pa}
\)
Initial volume, \(V_{1}=1 \mathrm{~m}^{3}\)
\(
\text {Final volume, } \begin{aligned}
V_{2} &=10 \times 10^{-3} \mathrm{~m}^{3}=10^{-2} \mathrm{~m}^{3} \\
W &=p \Delta V \\
&=10^{5}\left(1-10^{-2}\right)=99,000 \mathrm{~J}
\end{aligned}
\)
\(
\text {pressure, } p=100 \mathrm{kPa}=10^{5} \mathrm{~Pa}
\)
Initial volume, \(V_{1}=1 \mathrm{~m}^{3}\)
\(
\text {Final volume, } \begin{aligned}
V_{2} &=10 \times 10^{-3} \mathrm{~m}^{3}=10^{-2} \mathrm{~m}^{3} \\
W &=p \Delta V \\
&=10^{5}\left(1-10^{-2}\right)=99,000 \mathrm{~J}
\end{aligned}
\)
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