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Question

It is found that when a certain gas is heated, its volume increases by $$50$$% and pressure decreases to $$75$$% of its original value. If the original temperature of the gas was $$-{15}^{o}C$$, find the temperature(in Celsius) to which of it was heated:


Solution

Initial volume=$$V_{1}$$, pressure=$$P_{1}$$ and temperature=$$T_{1}$$.
Final Volume=$$V_{2}=\cfrac{150}{100}=1.5V_{1}$$ as volume increases by 50%.
Final Pressure=$$P_{2}=0.75P_{1}$$ as pressure decreases to 75% of its original pressure.
Original temperature=$$T_{1}$$=-15$$^{\circ}$$C=258 K
Now, $$\cfrac{PV}{T}=nR$$= constant for a particular gas having 1 mole.
$$\cfrac { { P }_{ 1 }{ V }_{ 1 } }{ { T }_{ 1 } } =\cfrac { { P }_{ 2 }{ V }_{ 2 } }{ { T }_{ 2 } } $$
$$\Longrightarrow \cfrac { { P }_{ 1 }{ V }_{ 1 } }{ 258 } =\cfrac { { 0.75P }_{ 1 }\times 1.5{ V }_{ 1 } }{ { T }_{ 2 } } \Longrightarrow { T }_{ 2 }=$$290.25 K=17.25$$^{\circ}$$C


Physics

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