A raindrop (mass=1.00g) is travelling at a speed of 40m/s when it hits the surface of 100g of water contained in a drinking glass. What is the change in temperature of the water in the glass if we assume that i)all the kinetic energy of the raindrop is converted to energy that changes the water's temperature, and ii)the water in the glass and the raindrop were at the same original temperature?

Question

A raindrop (mass=1.00g) is travelling at a speed of 40m/s when it hits the surface of 100g of water contained in a drinking glass. What is the change in temperature of the water in the glass if we assume that i)all the kinetic energy of the raindrop is converted to energy that changes the water's temperature, and ii)the water in the glass and the raindrop were at the same original temperature?

I found the kinetic energy of the raindrop, but I don't know what to do after that. Please help. Thanks.

Answer 1

To find the change in temperature of the water in the glass, you need to use the concept of heat transfer. Specifically, you need to calculate the heat transferred from the raindrop to the water in order to determine the change in temperature.

To begin, let's use the equation for kinetic energy:

Kinetic Energy = (1/2) * mass * (speed^2)

Given that the mass of the raindrop is 1.00g and its speed is 40m/s, we can calculate its kinetic energy as follows:

Kinetic Energy of raindrop = (1/2) * 0.001kg * (40m/s)^2

Now that you have the kinetic energy of the raindrop, you can move on to calculating the heat transferred. The heat transferred is equal to the change in internal energy of the water. In this case, we assume that all the kinetic energy of the raindrop is converted into energy that changes the water's temperature.

The equation relating the heat transferred to the change in temperature is given by:

Q = m * c * ΔT

where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Given that the mass of the water in the glass is 100g (0.1kg) and the specific heat capacity of water is 4.18 J/g·°C, we can substitute these values into the equation:

Kinetic Energy of raindrop = Q = m * c * ΔT

(1/2) * 0.001kg * (40m/s)^2 = 0.1kg * 4.18 J/g·°C * ΔT

Simplifying the equation, we can solve for ΔT:

(1/2) * 40^2 J = 0.1 * 4.18 * ΔT

800 J = 0.418 J/°C * ΔT

ΔT = 800 J / (0.418 J/°C)

After performing the division, you will find the value of ΔT, which represents the change in temperature of the water in the glass.

Note: Be careful with the units to ensure they are consistent throughout the calculations.

Answer 2

change in heat to glass= KE of the raindrop

but
changeinheat=.100*specificheatwater(deltaTemp)

solve for changeinTemp

b. same, except change the mass to .101kg