Question

The pressure of a definite mass of a gas is directly proportional to the temperature and inversely proportional to the volume under the given conditions. If the temperature is increased by $40\%$ and the volume is decreased by $20\%$ then the new pressure will:

• A. Be increased by $75\%$
• B. Reduce to $25\%$
• C. Be increased by $20\%$
• D. Increased by $28\%$

Answer 1

Answer: (A)

Be increased by $75\%$

Let the initial pressure be $100$

Given: Temperature increases by $40\%$.

$\therefore$ pressure increases by $40$% according to the question.

New pressure:

$=100+\frac{100\times 40}{100}=140$

Now, if volume decreases by $20\%$ then pressure increases by 20%.

Since, volume is inversely proportional to pressure

New pressure:

$=\frac{140}{\frac{100-20}{100}}=\frac{140\times 100}{80}=175$

Then, pressure will increase from $100$ to $175$.

Therefore, pressure will increase by $175-100=75\%$