Question

practice questions

1. when equal masses of x and y absorb the same amount of energy, their temperatures rise by 5°c and 10°c respectively. which is correct?

a the specific heat capacity of x is twice that of y.
b the specific heat capacity of x is half that of y.
c the specific heat capacity of x is one fifth that of y.
d the specific heat capacity of x is the same as y.

1. a pure aluminium block with a mass of 10g is heated so that its temperature increases from 20°c to 50°c. the specific heat capacity of aluminium is 8.99×10⁻¹jg⁻¹k⁻¹. which expression gives the heat energy change in kj?

a 10×8.99×10⁻¹×303
b 10×8.99×10⁻¹×30
c (10×8.99×10⁻¹×303)/1000
d (10×8.99×10⁻¹×30)/1000

Explanation:

Step1: Recall heat - energy formula

The heat - energy formula is $Q = mc\Delta T$, where $Q$ is the heat energy, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature.

Step2: Solve for question 1

Let the mass of $X$ and $Y$ be $m$, the specific heat capacity of $X$ be $c_X$ and of $Y$ be $c_Y$, the change in temperature of $X$ be $\Delta T_X=5^{\circ}C$ and of $Y$ be $\Delta T_Y = 10^{\circ}C$. Since $Q_X = Q_Y$, we have $m\times c_X\times\Delta T_X=m\times c_Y\times\Delta T_Y$. Canceling out $m$ on both sides, we get $c_X\times5 = c_Y\times10$, so $c_X = 2c_Y$.

Step3: Solve for question 2

First, calculate the change in temperature $\Delta T=50 - 20=30^{\circ}C$. The heat - energy formula is $Q = mc\Delta T$. Here, $m = 10g$, $c = 8.99\times10^{-1}Jg^{-1}K^{-1}$, and $\Delta T = 30K$ (since a change in Celsius is the same as a change in Kelvin for temperature differences). The heat energy $Q$ in joules is $Q=10\times8.99\times10^{-1}\times30J$. To convert to kilojoules, divide by 1000, so $Q=\frac{10\times8.99\times10^{-1}\times30}{1000}kJ$.

Answer:

1. A. The specific heat capacity of X is twice that of Y.
2. D. $\frac{10\times8.99\times10^{-1}\times30}{1000}$