Thermodynamics First Law Principle
The First Law of Thermodynamics relates heat, work, and internal energy. For a system, the rate of change of internal energy is equal to the rate at which heat is supplied minus the rate at which work is done by the system.
Mathematically, this is expressed as: $ \frac{dU}{dt} = \frac{dQ}{dt} - \frac{dW}{dt} $ Or using rate notation: $ \dot{U} = \dot{Q} - \dot{W} $ Where:
- $ \dot{U} $ is the rate of change of internal energy (in Watts, W).
- $ \dot{Q} $ is the rate of heat supplied to the system (in Watts, W).
- $ \dot{W} $ is the rate of work done by the system (in Watts, W or Joules per second, J/s).
Calculating Rate of Internal Energy Increase
Given:
- Rate of heat supplied, $ \dot{Q} = 100 \text{ W} $.
- Rate of work done by the system, $ \dot{W} = 75 \text{ J/s} = 75 \text{ W} $.
Substitute the given values into the First Law equation:
$ \dot{U} = 100 \text{ W} - 75 \text{ W} $ $ \dot{U} = 25 \text{ W} $Therefore, the rate at which the internal energy of the system increases is $ 25 \text{ W} $.
Answer Selection
The calculated rate of increase in internal energy is $ 25 \text{ W} $, which corresponds to Option D.
Similar Questions
A flask contains argon and chlorine in the ratio of $2:1$ by mass. The temperature of the mixture is $27^\circ\text{C}$. The ratio of root mean square speed of the molecules of the two gases $(\frac{V_{rms}^{Ar}}{V_{rms}^{Cl}})$ is :
(Atomic mass of argon = $40 \text{ u}$ and molecular mass of chlorine = $70 \text{ u}$)- The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If number densities of the gases A and B are $n_A$ and $n_B$, respectively, then the correct option is :
- In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas ($\gamma = 5/3$) decreases from $60\text{K}$ to $50\text{K}$. The work done by the gas in the process is :
(Take the universal gas constant as $R = 8.3\text{ J mol}^{-1}\text{ K}^{-1}$) One mole of an ideal monatomic gas undergoes a cyclic process as shown in the figure. The total heat supplied to the gas is :
- An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $f$ number of vibrational modes. If the ratio of heat capacities $C_P/C_V$ of the gas is 8/7, then the value of $f$ is :
Important Questions from Heat and Thermodynamics
- Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^\circ\text{C}$ to $120^\circ\text{C}$ ?
- $10 \text{ kg}$ of ice at $-10^\circ\text{C}$ is added to $100 \text{ kg}$ of water to lower its temperature from $25^\circ\text{C}$. Consider no heat exchange to surroundings. The decrement to the temperature of water is ________$^\circ\text{C}$.
(specific heat of ice = $2100 \text{ J/Kg.}^\circ\text{C}$, specific heat of water = $4200 \text{ J/Kg.}^\circ\text{C}$, latent heat of fusion of ice = $3.36 \times 10^5 \text{ J/Kg}$) - The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{\text{th}}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ($\Delta Q = 0$) then identify the gas from the following options (Assuming the gases given in the options are ideal gases):
Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100^\circ\text{C}$ and $40^\circ\text{C}$ respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperature at junction points $B$ and $E$ are (close to):
- Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is $32 \times 10^{18}$ /s then collision frequency in gas A is _________ /s.
