An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately. (Latent heat of fusion of ice is \(3.4 × 10^5\) \(J kg^{–1 }\)and thermal conducting of insulation wall is \(0.05\) \(Wm^{–1}\)°\(C^{–1})\)
- \(61 \times 10^{-3}kgs^{-1}\)
- \(61 \times 10^{-5}kgs^{-1}\)
- \(208\;kgs^{-1}\)
- \(30 \times 10^{-3}kgs^{-1}\)
The Correct Option is B
Solution and Explanation
The rate of melting of ice is :
\(\frac{Δ_Q}{Δ_t} = \frac{kA(T_1-T_2)}{l}\)
\(⇒ \frac{mL}{Δt} = \frac{kA(T_1-T_2)}{l}\)
\(⇒ \frac{m}{Δt} = \frac{kA(T_1-T_2)}{Ll}\)
\(\approx 61.1 \times 10^{-5} kg/s\)
Hence, the correct option is (B): \(61 \times 10^{-5}kgs^{-1}\)
Top Questions on Thermodynamics
- In a Carnot engine, efficiency is dependent on ________?
- KEAM - 2025
- Physics
- Thermodynamics
The ratio of the fundamental vibrational frequencies \( \left( \nu_{^{13}C^{16}O} / \nu_{^{12}C^{16}O} \right) \) of two diatomic molecules \( ^{13}C^{16}O \) and \( ^{12}C^{16}O \), considering their force constants to be the same, is ___________ (rounded off to two decimal places).}
- GATE CY - 2025
- Chemistry
- Thermodynamics
- The translational, vibrational, and rotational molecular partition functions for a system containing ideal diatomic gas molecules in the canonical ensemble (N, V, T) are written as \( q_{{trans}}, q_{{vib}}, \) and \( q_{{rot}} \), respectively. The option that correctly defines their thermodynamic variable(s) dependency is:
- GATE CY - 2025
- Chemistry
- Thermodynamics
A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K. Heat loss from the auditorium is 15 kW. The power consumption of the heat pump is _________ kW (rounded off to 2 decimal places).
- The enthalpy change for the reaction \( \text{C}_2\text{H}_4 (\text{g}) + 3\text{O}_2 (\text{g}) \rightarrow 2\text{CO}_2 (\text{g}) + 2\text{H}_2\text{O} (\text{l}) \) is \( -1410 \, \text{kJ/mol} \). If the standard enthalpies of formation of \( \text{CO}_2 (\text{g}) \) and \( \text{H}_2\text{O} (\text{l}) \) are \( -393.5 \, \text{kJ/mol} \) and \( -286 \, \text{kJ/mol} \) respectively, what is the standard enthalpy of formation of \( \text{C}_2\text{H}_4 (\text{g}) \)?
- MHT CET - 2025
- Chemistry
- Thermodynamics
Questions Asked in JEE Main exam
If $10 \sin^4 \theta + 15 \cos^4 \theta = 6$, then the value of $\frac{27 \csc^6 \theta + 8 \sec^6 \theta}{16 \sec^8 \theta}$ is:
- JEE Main - 2025
- Trigonometric Identities
If the area of the region $\{ (x, y) : |x - 5| \leq y \leq 4\sqrt{x} \}$ is $A$, then $3A$ is equal to
- JEE Main - 2025
- Area between Two Curves
Let $A = \begin{bmatrix} \cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta \end{bmatrix}$. If for some $\theta \in (0, \pi)$, $A^2 = A^T$, then the sum of the diagonal elements of the matrix $(A + I)^3 + (A - I)^3 - 6A$ is equal to
- JEE Main - 2025
- Matrices
Let $A = \{ z \in \mathbb{C} : |z - 2 - i| = 3 \}$, $B = \{ z \in \mathbb{C} : \text{Re}(z - iz) = 2 \}$, and $S = A \cap B$. Then $\sum_{z \in S} |z|^2$ is equal to
- JEE Main - 2025
- Determinants
Let $C$ be the circle $x^2 + (y - 1)^2 = 2$, $E_1$ and $E_2$ be two ellipses whose centres lie at the origin and major axes lie on the $x$-axis and $y$-axis respectively. Let the straight line $x + y = 3$ touch the curves $C$, $E_1$, and $E_2$ at $P(x_1, y_1)$, $Q(x_2, y_2)$, and $R(x_3, y_3)$ respectively. Given that $P$ is the mid-point of the line segment $QR$ and $PQ = \frac{2\sqrt{2}}{3}$, the value of $9(x_1 y_1 + x_2 y_2 + x_3 y_3)$ is equal to
- JEE Main - 2025
- Coordinate Geometry
Concepts Used:
Thermodynamics
Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter.
Important Terms
System
A thermodynamic system is a specific portion of matter with a definite boundary on which our attention is focused. The system boundary may be real or imaginary, fixed or deformable.
There are three types of systems:
- Isolated System – An isolated system cannot exchange both energy and mass with its surroundings. The universe is considered an isolated system.
- Closed System – Across the boundary of the closed system, the transfer of energy takes place but the transfer of mass doesn’t take place. Refrigerators and compression of gas in the piston-cylinder assembly are examples of closed systems.
- Open System – In an open system, the mass and energy both may be transferred between the system and surroundings. A steam turbine is an example of an open system.
Thermodynamic Process
A system undergoes a thermodynamic process when there is some energetic change within the system that is associated with changes in pressure, volume and internal energy.
There are four types of thermodynamic process that have their unique properties, and they are:
- Adiabatic Process – A process in which no heat transfer takes place.
- Isochoric Process – A thermodynamic process taking place at constant volume is known as the isochoric process.
- Isobaric Process – A process in which no change in pressure occurs.
- Isothermal Process – A process in which no change in temperature occurs.
Laws of Thermodynamics
Zeroth Law of Thermodynamics
The Zeroth law of thermodynamics states that if two bodies are individually in equilibrium with a separate third body, then the first two bodies are also in thermal equilibrium with each other.
First Law of Thermodynamics
The First law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter transfer, and relating them to a function of a body's state, called internal energy.
Second Law of Thermodynamics
The Second law of thermodynamics is a physical law of thermodynamics about heat and loss in its conversion.
Third Law of Thermodynamics
Third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: The entropy of a system approaches a constant value when its temperature approaches absolute zero.