Question

You leave a pastry in the refrigerator on a plate and ask your roommate to take it out before you get home so you can eat it at room temperature, the way you like it. Instead, your roommate plays video games for hours. When you return, you notice that the pastry is still cold, but the game console has become hot. Annoyed, and knowing that the pastry will not be good if it is microwaved, you warm up the pastry by unplugging the console and putting it in a clean trash bag (which acts as a perfect calorimeter) with the pastry on the plate. After a while, you find that the equilibrium temperature is a nice, warm (38.3°C). You know that the game console has a mass of (2.1 kg). Approximate it as having a uniform initial temperature of (45°C). The pastry has a mass of (0.16 kg) and a specific heat of (3.0 kJ/(kg·ºC)), and is at a uniform initial temperature of (4.0°C). The plate is at the same temperature and has a mass of (0.24 kg) and a specific heat of (0.90 kJ/(kg·ºC)). What is the specific heat of the console?

a) Calculate the specific heat of the game console.
b) Discuss the concept of specific heat and its applications.

Answer 1

The specific heat of the game console can be calculated using the conservation of energy principle by equating the heat lost by the console to the heat gained by the pastry and plate when they reach thermal equilibrium. The specific heat is a fundamental property used in many practical applications, including climate science and culinary arts.

Step-by-step explanation:

Specific Heat of the Game Console

To find the specific heat of the game console, we apply the principle of conservation of energy where the heat lost by the console is equal to the heat gained by the pastry and the plate combined when they reach thermal equilibrium.

The heat lost by the console (Q_console) can be expressed as:

Q_console = m_console * c_console * ΔT_console

Where m_console is the mass of the console, c_console is the specific heat of the console, and ΔT_console is the change in temperature of the console.

The heat gained by the pastry (Q_pastry) and the plate (Q_plate) can be expressed as:

Q_pastry = m_pastry * c_pastry * ΔT_pastry

Q_plate = m_plate * c_plate * ΔT_plate

By setting Q_console equal to the sum of Q_pastry and Q_plate and rearranging for c_console, we can calculate the specific heat of the console.

Specific Heat, c, of a substance is the amount of heat required to change the temperature of one kilogram of the substance by one degree Celsius. It is a property that can vary with temperature and the phase of the material, but for this calculation, we will consider it as a constant.

The specific heat concept is significant in various applications, such as designing heating and cooling systems, understanding and predicting climate change, and in culinary arts for cooking and refrigeration.