At temperatures close to 0 K, the heat capaci | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The rate of heat supply is constant, so $\frac{dQ}{dt} = P$ (where $P$ is a constant).By definition, $C = \frac{dQ}{dT}$, so $dQ = C \cdot dT = aT

Vedclass · Accepted Answer

Vedclass · Answer

(C) The rate of heat supply is constant, so $\frac{dQ}{dt} = P$ (where $P$ is a constant).By definition, $C = \frac{dQ}{dT}$, so $dQ = C \cdot dT = aT^3 \cdot dT$.Substituting this into the rate equation: $\frac{dQ}{dt} = aT^3 \frac{dT}{dt} = P$.Rearranging gives $T^3 \cdot dT = \frac{P}{a} \cdot dt$.Integrating both sides: $\int T^3 \cdot dT = \int \frac{P}{a} \cdot dt$.This yields $\frac{T^4}{4} = \frac{P}{a} \cdot t + 	ext{constant}$.Assuming $T = 0$ at $t = 0$, the constant is $0$, so $T^4 = \frac{4P}{a} \cdot t$.Thus, $T = \left( \frac{4P}{a} ight)^{1/4} \cdot t^{1/4}$.Since $T \propto t^{1/4}$, the graph of $T$ versus $t$ will be a curve that starts at the origin and has a decreasing slope as $t$ increases (concave down), which corresponds to Graph $C$.

Similar Questions

The heat energy released by water of mass $2 \,kg$ when it is cooled by $10^{\circ} C$ is (Specific heat capacity of water $= 4200 \,J \,kg^{-1} \,K^{-1}$) (in $\,J$)

What is the value of the specific heat of a solid by using the law of equipartition of energy?

Heat energy at a constant rate is supplied to two substances $P$ and $Q$. If the variation of temperature $(T)$ of the substances with time $(t)$ is as shown in the figure,then select the correct statement.

$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet, the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

If some heat is given to a metal of mass $100 \ g$,its temperature rises by $20^{\circ} C$. If the same heat is given to $20 \ g$ of water,the change in its temperature (in $^{\circ} C$) is (The ratio of specific heat capacities of metal and water is $1: 10$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module