A given mass of gas has a pressure of 80 Nm\(^{-2}\) at a temperature of 47 C. If the temperature is reduced to 27 C with volume remaining constant, the new pressure is?
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Correct Answer: Option B
Explanation:
Using \(\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}\)
P\(_{1}\) = 80Nm\(^{2}\)
T\(_{1}\) = 47 + 273 = 320k
T\(_{2}\) = 27 + 273 = 300k
P\(_{2}\)?
\(\therefore\) = P\(_{2}\) = \(\frac{P_{1}T_{2}}{T_{1}}\)
= \(\frac{80 \times 300}{320}\) = 75.Nm\(^{2}\)
Using \(\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}\)
P\(_{1}\) = 80Nm\(^{2}\)
T\(_{1}\) = 47 + 273 = 320k
T\(_{2}\) = 27 + 273 = 300k
P\(_{2}\)?
\(\therefore\) = P\(_{2}\) = \(\frac{P_{1}T_{2}}{T_{1}}\)
= \(\frac{80 \times 300}{320}\) = 75.Nm\(^{2}\)