Fill in the blanks:
$1.$ The heat required to raise the temperature of a body by $1\,K$ is called ...... .
$2.$ $A$ temperature difference of $10\,^{\circ}C$ is equivalent to a temperature difference of ...... on the Fahrenheit temperature scale.
$3.$ For an isothermal process of an ideal gas,$\frac{dP}{P} = .........$

(N/A) $1.$ The heat required to raise the temperature of a body by $1\,K$ is defined as its thermal capacity.
$2.$ The relation between temperature differences is $\Delta T_F = \frac{9}{5} \Delta T_C$. Given $\Delta T_C = 10\,^{\circ}C$,then $\Delta T_F = \frac{9}{5} \times 10 = 18\,^{\circ}F$.
$3.$ For an isothermal process,$PV = \text{constant}$. Differentiating both sides,we get $P dV + V dP = 0$. Rearranging gives $V dP = -P dV$,which simplifies to $\frac{dP}{P} = -\frac{dV}{V}$.