A piece of glass has a temperature of 72.0 °C. Liquid that has a temperature of 37.0 °C is poured over the glass, completely covering it, and the temperature at equilibrium is 50.0 °C. The mass of the glass and the liquid is the same. Ignoring the container that holds the glass and liquid and assuming that the heat lost to or gained from the surroundings is negligible, determine the specific heat capacity of the liquid.

You need more information. You need the specific heat of the glass in order to calculate the specific heat of the liquid. The information you provided will only tell you the ratio of speciic heats

the specific heat of the glass is 840 J/kg*C, it's in one of the tables in the book but it's really stupid how they don't give that with the problem

To determine the specific heat capacity of the liquid, we need to use the principle of conservation of energy. This principle states that the heat lost by the hot object is equal to the heat gained by the cold object until they reach thermal equilibrium.

In this case, the glass loses heat as its temperature decreases from 72.0 °C to 50.0 °C, while the liquid gains heat as its temperature increases from 37.0 °C to 50.0 °C.

The heat lost by the glass can be calculated using the formula:

Qglass = mcΔT

Where:
Qglass = heat lost by the glass
m = mass of the glass
c = specific heat capacity of the glass
ΔT = change in temperature for the glass (72.0 °C - 50.0 °C)

The heat gained by the liquid can be calculated using the formula:

Qliquid = mcΔT

Where:
Qliquid = heat gained by the liquid
m = mass of the liquid
c = specific heat capacity of the liquid
ΔT = change in temperature for the liquid (50.0 °C - 37.0 °C)

Since the mass of the glass and liquid is the same, we can equate the two equations:

mcΔT = mcΔT

Canceling the mass from both sides of the equation, we get:

cΔTglass = cΔTliquid

Substituting the values, we have:

c (72.0 °C - 50.0 °C) = c (50.0 °C - 37.0 °C)

Now, we solve for c:

22.0 c = 13.0 c

Dividing both sides by 13.0 c, we get:

22.0 = 13.0

Since this equation is not true, we have a contradiction. Therefore, our assumption that the mass of the glass and liquid is the same is incorrect.

To determine the specific heat capacity of the liquid, we need additional information, such as the masses of the glass and the liquid. Without this information, we cannot calculate the specific heat capacity of the liquid.