Question

The thermal capacity of $10\,g$ of a substance is $8\,cal/kelvin$. Its specific heat is in_____ J/kg−k.
A. 3360
B. 3600
C. 6330
D. 3036

Answer 1

Heat capacity, also known as thermal capacity, is a physical attribute of matter defined as the amount of heat required to cause a unit change in temperature in a given quantity of material. The joule per kelvin (J/K) is the SI unit for heat capacity. The term "heat capacity" refers to a wide range of characteristics. The specific heat capacity is the intense feature that corresponds. The molar heat capacity is calculated by dividing the heat capacity by the quantity of material in moles.

Formula used:
$C = \frac{{\Delta Q}}{m}$
Here $C$ = specific heat capacity, $M$ = mass and $\Delta Q$= thermal capacity.

Complete step by step answer:
Start with the item at a known uniform temperature, add a known amount of heat energy to it, wait for its temperature to become uniform, and measure the change in temperature. For many substances, this approach can produce quite accurate results; but, it cannot produce extremely exact readings, particularly for gases. The vast majority of physical systems have a positive heat capacity. However, despite what may appear to be a contradiction at first, certain systems have a negative heat capacity.

The thermal capacity of 10g of a substance is 8cal/c.
Given $m=10\,g$
$\Delta Q = 8cal/c$
To convert 8 cal/c to j/kg. We should multiply 8 with $(\frac{{4.2}}{{10}}) \times {10^3}$.
We know that $C = \frac{{\Delta Q}}{m}$
$C = 8 \times 4.2 x 100 \\\ \Rightarrow C = 80 \times 42$
$\therefore C = 3360\,J{K^{ - 1}}$

Hence, the correct answer option A.

Note: While working on the problems, keep in mind the conversion factor. When two systems with differing temperatures interact via a purely thermal connection, heat flows from the hotter system to the cooler one, according to the Second Law of Thermodynamics (this can also be understood from a statistical point of view). As a result, if the temperatures of such systems are identical, they are in thermal equilibrium. This equilibrium, however, is only stable if the systems have positive heat capacity.