A perfectly insulated cup is filled with water initially at 20C. Heat energy is transferred to the cup by an immersion heater at a steady rate. Sketch on the axes that follow the temp as a function of time. Explain the shape of your graph and write down a mathematical relationship for the temperature as a function of the quantity of heat energy (Q) that has been transferred to the water.

i have T=Q/mc, is this right?

(T-To) = Q/mc, but they are interested in temperature (T) vs time, not vs Q.

Power(P) = dQ/dt is a rate at which heat is added

P/(mc) is the slope of the T vs t curve, which will be a straight line ramping upwards.

T = To + (P/mc)*t

Well, if we assume that the heat capacity (c) and mass (m) of the water remain constant, then yes, your equation T = Q/(mc) is a reasonable relationship between temperature (T) and the quantity of heat energy (Q) transferred to the water.

As for the graph, it would essentially show a linear increase in temperature over time. Initially, the temperature will rise rapidly as heat energy is transferred to the water, but as time goes on, the temperature increase will become slower due to the insulating properties of the cup. Eventually, the temperature will reach a point where it stops increasing and levels off when the heat being transferred in balances out with the heat being lost to the surroundings.

So, to summarize, your graph would show an initially steep linear increase in temperature that gradually levels off until it reaches a steady state.

Yes, T=Q/mc is the correct relationship. Here, T represents temperature, Q represents the quantity of heat energy transferred, m represents the mass of the water, and c represents the specific heat capacity of the water.

To sketch the graph of temperature as a function of time, we need to take into consideration the relationship between heat energy and temperature. According to the relationship T=Q/mc, as heat energy is transferred to the water, the temperature will increase.

Initially, the temperature of the water is 20°C. As the immersion heater continues to transfer heat energy to the water, the temperature will rise. However, since the cup is perfectly insulated, there is no heat loss to the surroundings, so the temperature will continually increase until it reaches a maximum value.

Therefore, the graph will show a steady increase in temperature over time until it reaches a maximum value, and then it will remain constant.

On the y-axis, we have the temperature in °C, and on the x-axis, we have time in seconds. The graph will have an increasing slope until it levels off to a horizontal line at the maximum temperature reached.

Note: The specific values on the graph will depend on the specific details of the system, such as the rate at which heat energy is transferred to the water and the specific heat capacity of the water.

Yes, you are on the right track! The equation T = Q/mc is the correct equation to describe the relationship between temperature (T), heat energy transferred (Q), mass of the water (m), and the specific heat capacity of water (c).

To explain the shape of the graph, let's go through the equation step by step. T = Q/mc tells us that the temperature is directly proportional to the amount of heat energy transferred (Q). This means that as more heat energy is transferred to the water, the temperature will increase.

However, the equation also includes the mass of the water (m) and the specific heat capacity of water (c). The mass tells us that the more water there is, the more heat energy will be required to increase the temperature. The specific heat capacity tells us that water requires a high amount of heat energy to increase in temperature compared to some other substances.

As a result, the graph will initially start with a steep increase in temperature as heat energy is transferred. This is because at the beginning, the water is at a lower temperature and has not absorbed much heat yet. However, as time goes on and more heat energy is transferred, the rate of temperature increase will slow down. This is because the water becomes warmer and requires more heat energy to achieve further temperature increases.

The shape of the graph can be roughly illustrated as an upward sloping curve that gradually levels off as time progresses.

As for the mathematical relationship you mentioned, T = Q/mc, it is indeed correct. This equation states that the temperature (T) is equal to the heat energy transferred (Q) divided by the product of the mass (m) of the water and the specific heat capacity (c) of water. It can be rearranged as Q = m * c * T to solve for the amount of heat energy transferred.