MHT CET · Physics · Thermal Properties of Matter
A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two end conduct an amount of heat ' \(Q_1\) ' in time ' \(t\) ' the metallic rod is melted and the material is formed into a rod of length four times the length of original rod. The amount of heat conducted by the new rod when placed in thermal contact with the same two reservoirs in time \(t\) is ' \(Q_2\) '. Then \(\frac{Q_1}{Q_2}\) is
- A \(16\)
- B \(\frac{1}{16}\)
- C \(\frac{1}{4}\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
The heat conduction rate is given by:
\(\frac{Q}{t}=\frac{k A\left(T_1-T_2\right)}{l}\)
Considering volume conservation:
\(\begin{aligned} & A_1 l_1=A_2 l_2 \\ & A_1 l_1=A_2\left(4 l_1\right) \\ & \Rightarrow A_2=\frac{A_1}{4} \\ & \frac{Q_2}{t}=\frac{k\left(\frac{A_1}{4}\right)\left(T_1-T_2\right)}{4 l_1}=\frac{1}{16} \frac{k A_1\left(T_1-T_2\right)}{l_1}=\frac{1}{16} \frac{Q_1}{t} \\ & \Rightarrow Q_2=\frac{1}{16} Q_1\end{aligned}\)
\(\frac{Q}{t}=\frac{k A\left(T_1-T_2\right)}{l}\)
Considering volume conservation:
\(\begin{aligned} & A_1 l_1=A_2 l_2 \\ & A_1 l_1=A_2\left(4 l_1\right) \\ & \Rightarrow A_2=\frac{A_1}{4} \\ & \frac{Q_2}{t}=\frac{k\left(\frac{A_1}{4}\right)\left(T_1-T_2\right)}{4 l_1}=\frac{1}{16} \frac{k A_1\left(T_1-T_2\right)}{l_1}=\frac{1}{16} \frac{Q_1}{t} \\ & \Rightarrow Q_2=\frac{1}{16} Q_1\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A metal ball of radius \(9 \times 10^{-4} \mathrm{~m}\) and density \(10^4 \mathrm{~kg} / \mathrm{m}^3\) falls freely under gravity through a distance 'h' and erfters a tank of water. Considering that the metal ball has constant velocity, the value of h is [coefficient of viscosity of water \(=8.1 \times 10^{-4} \mathrm{pa}-\mathrm{s}, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) density of water \(\left.=10^3 \mathrm{~kg} / \mathrm{m}^3\right]\)MHT CET 2024 Hard
- If \(\mathrm{p}-\mathrm{n}\) junction diode is in forward bias thenMHT CET 2023 Easy
- When an observer moves towards a stationary source with velocity ' \(\mathrm{V}_1\) ', the appearent frequency of emitted note is ' \(\mathrm{F}_1\) '. When observer moves away from stationary source with velocity ' \(\mathrm{V}_1\) ' the appearent frequency is ' \(F_2\) '. If ' \(v\) ' is velocity of sound in air and \(\frac{F_1}{F_2}=2\), then \(\frac{V}{V_1}\) is equal toMHT CET 2025 Medium
- An electron of stationary Hydrogen atom passes from fifth energy level to ground level. The velocity that the atom acquired as a result of photo emission is
( \(\mathrm{m}=\) mass of electron, \(\mathrm{R}=\) Rydberg's constant)
( \(\mathrm{h}=\) Planck's constant)MHT CET 2024 Medium - In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged \((\mathrm{Q})\) is \(\left(\gamma=\frac{C_p}{C_v}\right)\)MHT CET 2024 Medium
- A charge \(17.7 \times 10^{-4} \mathrm{C}\) is distributed uniformly over a large sheet of area \(200 \mathrm{~m}^2\). The electric field intensity at a distance \(20 \mathrm{~cm}\) from it in air will be \(\left[\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\right]\)MHT CET 2023 Medium
More PYQs from MHT CET
- Determine the expected value of \(\Delta \mathrm{T}_{\mathrm{f}}\) for \(1 \mathrm{~m}\) \(\mathrm{CaCl}_2\) solution if 1 m urea solution has \(\Delta \mathrm{T}_{\mathrm{f}}\) value ' \(x\) ' K .MHT CET 2025 Medium
- The order and degree of the differential equation \(\sqrt{1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}}=\left(\frac{d^{2} y}{d x^{2}}\right)^{\frac{3}{2}}\) are respectivelyMHT CET 2020 Easy
- A convex lens of focal length ' \(f\) ' produces a real image whose size is ' \(n\) ' times the size of an object. The distance of the object from the lens isMHT CET 2024 Easy
- The equation to the line touching both the parabolas \(y^{2}=4 x\) and \(x^{2}=-32 y\), isMHT CET 2007 Medium
- A boat is moving due east in a region where the earth's magnetic field is \(3.6 \times 10^{-5} \mathrm{~N} / \mathrm{Am}\) due north and horizontal. The boat carries a vertical conducting rod 2 m long. If the speed of the boat is \(2.00 \mathrm{~m} / \mathrm{s}\), the magnitude of the induced e.m.f. in the rod isMHT CET 2024 Easy
- The Henry's law constant for oxygen is \(1 \cdot 3 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~atm}^{-1}\). If partial pressure of oxygen is \(0.46\) atmosphere what is the concentration of dissolved oxygen at \(25^{\circ} \mathrm{C}\) and 1 atm pressure?MHT CET 2020 Easy