Heat, Work & First Law of Thermodynamics

An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of $75\text{ J/s}$, then the rate at which internal energy increases will be:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v\left(T_f - T_i\right) = \frac{nR}{\gamma-1}\left(T_f - T_i\right)$, where $\gamma = \frac{C_p}{C_v}, T_i =$ initial temperature, $T_f =$ final temperature. Statement II: Relation between degree of freedom $f$ and $\gamma\,(= C_p/C_v)$ is $\left(\gamma = 1 + \frac{2}{f}\right)$ Choose the correct answer from the options given below

An ideal gas having pressure P, volume V and temperature T undergoes a thermodynamic process in which $dW = 0$ and $dQ < 0$. Then, for the gas

An ideal gas having pressure P, volume V and temperature T undergoes a thermodynamic process in which $dW = 0$ and $dQ < 0$. Then, for the gas

One gram of a liquid is converted to vapour at $3 \times 10^{5}$ Pa pressure. If 10% of the heat supplied is used for increasing the volume by $1600$ cm$3$ during this phase change, then the increase in internal energy in the process will be

Given are statements for certain thermodynamic variables,

(A) Internal energy, volume $(V)$ and mass $(M)$ are extensive variables.

(B) Pressure (P), temperature ( T) and density ( $\rho$) are intensive variables.

(C) Volume (V), temperature (T) and density ( $\rho$) are intensive variables.

(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below:

During the melting of a slab of ice at 273 K at atmospheric pressure:

If heat energy $\Delta Q$ is supplied to an ideal diatomic gas, the increase in internal energy is $\Delta U$ and the amount of work done by the gas is $\Delta W$. The ratio $\Delta W : \Delta U : \Delta Q$ is

A source supplies heat to a system at the rate of $1000\text{ W}$. If the system performs work at a rate of $200\text{ W}$. The rate at which internal energy of the system increases is

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics $dQ = dU - dW$. Reason R: First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below:

$1\text{ kg}$ of water at $100^\circ\text{C}$ is converted into steam at $100^\circ\text{C}$ by boiling at atmospheric pressure. The volume of water changes from $1.00 \times 10^{-3}\text{ m}^{3}$ as a liquid to $1.671\text{ m}^{3}$ as steam. The change in internal energy of the system during the process will be

(Given latent heat of vaporisation $= 2257\text{ kJ/kg}$, Atmospheric pressure = $1 \times 10^{5}\text{ Pa})$

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer from the options given below

1 g of a liquid is converted to vapour at 3 $\times$ 10$5$ Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm$3$ during this phase change, then the increase in internal energy in the process will be:

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by 2.5 $\times$ 103 J?

Which one is the correct option for the two different thermodynamic processes?

The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0$^\circ$C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $\frac{x}{10}$. Then the value of x (round off to the nearest integer) is ___________. (Given R = 8.31 J mol${}^{-1}$ K${}^{-1}$)

1 g of water, of volume $1\text{ cm}^{3}$ at $100^\circ\text{C}$, is converted into steam at same temperature under normal atmospheric pressure ($\simeq 1 \times 10^{5}\text{ Pa}$). The volume of steam formed equals $1671\text{ cm}^{3}$. If the specific latent heat of vaporisation of water is $2256\text{ J/g}$, the change in internal energy is,

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $\ell$1, and that below the piston is $\ell$2, such that $\ell$1 > $\ell$2. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by:

(R is universal gas constant and g is the acceleration due to gravity)

A sample of 0.1 g of water at 100°C and normal pressure (1.013 × 105 N m–2) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample, is

The internal energy change in a system that has absorbed 2 kcal of heat and done 500 J of work is

Which of the following parameters does not characterize the thermodynamic state of mattter?

Which of the following is not thermodynamical function?

110 joule of heat is added to a gaseous system whose internal energy is 40 J, then the amount of external work done is

First law of thermodynamics is consequence of conservation of