For an ideal gas,the value of ${\left( {\frac{{dU}}{{dV}}} \right)_T}$ is ...... .

From the following plots,find the correct option.

Keeping temperature constant,the pressure of $11.2 \ dm^3$ of a gas was increased from $105 \ kPa$ to $420 \ kPa$. What is the new volume of the gas (in $dm^3$)?

The universal gas constant $R$ is defined as:

The following graph illustrates:

The volume and pressure of a balloon filled with hydrogen gas are $1 \ bar$ and $175 \ dm^{3}$. When the balloon reaches a certain height,its pressure decreases to $0.8 \ bar$. Calculate the new volume of the balloon. (in $dm^{3}$)