Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
According to Charles' law (1) \[{{\left( \frac{dV}{dT} \right)}_{p}}=K\] (2) \[{{\left( \frac{dT}{dV} \right)}_{p}}=K\] (3) \[{{\left( \frac{1}{T}-\frac{V}{{{T}^{2}}} \right)}_{p}}=0\] (4) \[V\propto \frac{1}{T}\]A) 1, 2 and 3 are correct
B) 1 and 2 are correct
C) 2 and 4 are correct
D) 1 and 3 are correct
Correct Answer: A
Solution :
According to Charles law \[V\propto t\]at constant p \[V=kT\]at constant p Or \[{{\left( \frac{dV}{dT} \right)}_{p}}=K\] Further, \[T\propto V\] \[T=KV\] Or \[{{\left( \frac{dT}{dV} \right)}_{p}}=K\] Further, \[\frac{V}{T}=K\] \[\frac{1}{T}.V=K\] Differentiating w.r.t. \[V\] \[{{\left( \frac{1}{T}-\frac{V}{{{T}^{2}}} \right)}_{p}}=0\]
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