Question

A box has two compartments of equal volume separated by a divider each compartment filled with a random sample of ${}^{\prime }n{}^{\prime }$ moles of a certain gas, but the pressure in compartment $A$ is twice the pressure in compartment $B$. Identify which of the following statements is true?

• A. The temperature in $A$ is twice the temperature in $B$
• B. The temperature in $B$ is twice the temperature in $A$
• C. The value of the ideal gas constant, $R$, in $A$ is twice the value of $R$ in $B$
• D. The temperature in $A$ is four times as great as the temperature in $B$
• E. The gas in $A$ is a heavier isotope than the gas in $B$

Answer 1

The correct option is A The temperature in $A$ is twice the temperature in $B$

Gaylussac's law states that at a constant temperature , pressure is directly proportional to temperature ,

$P\propto T$

the gas is closed in a box, therefore volume of gas is constant ,so temperature is proportional to pressure therefore when we double the pressure in compartment $A$ , temperature will also be doubled in compartment $A$ on the other hand pressure in $B$ is half of $A$ , so its temperature will be half of $A$ i.e. the temperature in $A$ is twice the temperature in $B$ .