The first law of thermodynamics

The first law of thermodynamics may be written as $\Delta U = q + w$. Say what the symbols $+\Delta U$, $+q$ and $+w$ mean in this equation.

Feb/March 2017

Inside a cylinder there are $5.12\,\text{mol}$ of an ideal gas at pressure $5.60 \times 10^5\,\text{Pa}$ and volume $3.80 \times 10^4\,\text{cm}^3$.

Feb/March 2018

A fixed mass of ideal gas occupies volume $V$ and has pressure $p$. The gas then completes the cycle X to Y to Z to X, as shown in Fig. 2.1. Table 2.1 gives the values of $p$, $V$ and temperature $T$ for the gas at points X, Y and Z.

Feb/March 2022

Using both kinetic energy and potential energy, explain the meaning of the internal energy of an ideal gas.

Feb/March 2024

The first law of thermodynamics can be written as $\Delta U = q + w$.

May/June 2011

The first law of thermodynamics can be written as $\Delta U = q + w$. Explain what the symbols $\Delta U$, $q$ and $w$ mean in this equation.

May/June 2011

The volume of an ideal gas inside a cylinder is $1.80 \times 10^{-3}\,\text{m}^3$ when the pressure is $2.60 \times 10^5\,\text{Pa}$ and the temperature is $297\,\text{K}$, as shown in Fig. 2.1. The thermal energy needed to increase the temperature by $1.00\,\text{K}$ of $1.00\,\text{mol}$ of the gas at constant volume is $12.5\,\text{J}$. The gas is then heated at constant volume so that the internal energy of the gas rises by $95.0\,\text{J}$.

May/June 2013

For $1.00\,\text{kg}$ of liquid water at $100\,^{\circ}\text{C}$, the volume is $1.00 \times 10^{-3}\,\text{m}^3$. For $1.00\,\text{kg}$ of water vapour at $100\,^{\circ}\text{C}$ and atmospheric pressure $1.01 \times 10^5\,\text{Pa}$, the volume is $1.69\,\text{m}^3$.

May/June 2014

A fixed mass of ideal gas has a volume of $3.49 \times 10^3\,\text{cm}^3$ at a temperature of $21.0^\circ\text{C}$. After heating, $565\,\text{J}$ of thermal energy makes it expand to a volume of $3.87 \times 10^3\,\text{cm}^3$ at $53.0^\circ\text{C}$. Fig. 2.1 shows this.

May/June 2014

The volume occupied by $1.00\,\text{kg}$ of water when it is a liquid at $100\,^{\circ}\text{C}$ is $1.00 \times 10^{-3}\,\text{m}^3$. For $1.00\,\text{kg}$ of water vapour at $100\,^{\circ}\text{C}$ and atmospheric pressure $1.01 \times 10^5\,\text{Pa}$, the volume is $1.69\,\text{m}^3$.

May/June 2014

A fixed mass of an ideal gas has a volume of $210\,\text{cm}^3$ when the pressure is $3.0 \times 10^5\,\text{Pa}$ and the temperature is $270\,\text{K}$. The gas volume is then lowered at constant pressure to $140\,\text{cm}^3$, as shown in Fig. 2.1. The final temperature of the gas is $T$.

May/June 2019

The first law of thermodynamics can be written as $\Delta U = q + w$.

May/June 2019

An ideal gas with a fixed mass occupies a volume of $210\ \text{cm}^{3}$ at a pressure of $3.0 \times 10^{5}\ \text{Pa}$ and a temperature of $270\ \text{K}$. Its volume is then decreased, while the pressure stays constant, to $140\ \text{cm}^{3}$, as illustrated in Fig. 2.1. The gas’s final temperature is $T$.

May/June 2019

Using the first law of thermodynamics, state and explain any change in the internal energy of:

May/June 2020

An ideal gas occupies a volume of $3.1 \times 10^{-3}\,\text{m}^3$ at a pressure of $8.5 \times 10^5\,\text{Pa}$ and a temperature of $290\,\text{K}$, as illustrated in Fig. 2.1. The gas then undergoes a sudden expansion to a volume of $6.3 \times 10^{-3}\,\text{m}^3$. No thermal energy is transferred during this expansion. Afterward, the gas has a pressure of $2.7 \times 10^5\,\text{Pa}$ and a temperature of $T_F$, as shown in Fig. 2.1.

May/June 2021

A fixed mass of ideal gas starts off at a temperature of $17^\circ\text{C}$. It occupies a volume of $0.24\,\text{m}^3$ and has a pressure of $1.2 \times 10^5\,\text{Pa}$.

May/June 2022

What does specific latent heat of vaporisation mean?

May/June 2022

At the start, a fixed mass of an ideal gas is at $17\,^{\circ}\text{C}$. Its volume is $0.24\,\text{m}^3$ and its pressure is $1.2 \times 10^5\,\text{Pa}$.

May/June 2022

State the first law of thermodynamics. Define any symbols that you use.

May/June 2023

Define specific heat capacity in terms of thermal energy, mass and temperature change.

May/June 2025

State the key assumption in the kinetic theory of gases that gives the result that the potential energy between the atoms of an ideal gas is zero.

Oct/Nov 2010

State the meaning of the internal energy of a system.

Oct/Nov 2013

A gas of fixed mass starts with a volume of $5.00 \times 10^{-4}\,\text{m}^3$ at a pressure of $2.40 \times 10^{5}\,\text{Pa}$ and a temperature of $288\,\text{K}$. It is then heated while the pressure stays constant, so that in the final state the volume becomes $14.5 \times 10^{-4}\,\text{m}^3$ and the temperature is $835\,\text{K}$, as shown in Fig. 3.1.

Oct/Nov 2014

State an expression, in terms of work done and heating, that is used to find the increase in internal energy of a system.

Oct/Nov 2015

State an expression, in terms of heating and work done, that is used to work out the increase in internal energy of a system.

Oct/Nov 2015

Two bodies are in thermal equilibrium. State what thermal equilibrium means.

Oct/Nov 2015

An ideal gas starts with pressure $1.0 \times 10^5\,\text{Pa}$, volume $4.0 \times 10^{-4}\,\text{m}^3$ and temperature $300\,\text{K}$, as shown in Fig. 2.1. A change in the gas’s energy of $240\,\text{J}$ causes the pressure to rise to a final value of $5.0 \times 10^5\,\text{Pa}$ while the volume stays constant. The thermodynamic temperature is now $T$.

Oct/Nov 2016

This question is about internal energy and thermodynamic processes.

Oct/Nov 2016

An ideal gas begins with pressure $1.0 \times 10^5\,\text{Pa}$, volume $4.0 \times 10^{-4}\,\text{m}^3$ and temperature $300\,\text{K}$, as shown in Fig. 2.1. A change in the gas’s energy of $240\,\text{J}$ raises the pressure to a final value of $5.0 \times 10^5\,\text{Pa}$ while the volume stays constant. The thermodynamic temperature is $T$.

Oct/Nov 2016

The first law of thermodynamics can be written as $\Delta U = (+q) + (+w)$, where $\Delta U$ is the increase in internal energy of the system. State the meaning of $+q$ and $+w$.

Oct/Nov 2020

State the meaning of the internal energy of a system.

Oct/Nov 2020

The first law of thermodynamics can be written as $\Delta U = (+q) + (+w)$, where $\Delta U$ is the rise in the internal energy of the system. State the meaning of: $+q$ and $+w$.

Oct/Nov 2020

Define specific heat capacity in precise terms.

Oct/Nov 2022

Define specific heat capacity in your own words.

Oct/Nov 2023

State what the term internal energy of a system means.

Oct/Nov 2023

State two ways in which the first law of thermodynamics shows how the internal energy of a system can be changed.

Oct/Nov 2025

A cylinder holds a fixed mass of an ideal gas at pressure $2Y$ and volume $6X$. The gas is taken through a series of changes from its starting state A, via states B, C and D, and then returns to its starting state A, as shown in Fig. 4.1. Fig. 4.2 displays how the internal energy of the gas varies with time.

Oct/Nov 2025

State two ways in which the first law of thermodynamics shows that a system’s internal energy may change.

Oct/Nov 2025