Question

the same amount of heat is added to five different liquids (+q) and the temperature change for each liquid is measured using a thermometer. given the temperature change for each liquid indicated in the image, which liquid has the largest heat capacity? assume no heat loss to the surroundings.
liquid a
liquid b
liquid c
liquid d
liquid e
dont test me yet, i am trying to gain an understanding before attempting to answer this question.

Explanation:

Step1: Recall the heat - capacity formula

The formula for heat is \(Q = mc\Delta T\), where \(Q\) is the heat added, \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the temperature change. Given that \(Q\) (heat added) and \(m\) (mass, since the amount of liquid is the same, assume \(m\) is constant) are the same for all liquids. We can rewrite the formula as \(c=\frac{Q}{m\Delta T}\). So, \(c\) is inversely proportional to \(\Delta T\) (\(c\propto\frac{1}{\Delta T}\))

Step2: Calculate the temperature change for each liquid

For Liquid A: \(\Delta T_A=28^{\circ}C\)
For Liquid B: \(\Delta T_B = 38^{\circ}C\)
For Liquid C: \(\Delta T_C=27^{\circ}C\)
For Liquid D: \(\Delta T_D=26^{\circ}C\)
For Liquid E: \(\Delta T_E = 34^{\circ}C\)

Step3: Determine the liquid with the largest heat capacity

Since \(c\propto\frac{1}{\Delta T}\), the liquid with the smallest \(\Delta T\) will have the largest \(c\). Comparing the \(\Delta T\) values: \(\Delta T_D(26^{\circ}C)<\Delta T_C(27^{\circ}C)<\Delta T_A(28^{\circ}C)<\Delta T_E(34^{\circ}C)<\Delta T_B(38^{\circ}C)\)

Answer:

Liquid D