A 385 g glass coffee cup is at a room temperature of 20◦C. It is then plunged into hot dishwater at 78◦C. If the temperature of the cup reaches that of the dishwater, how much heat does the cup absorb? Assume the mass of the dishwater is large enough so its temperature doesn’t change appreciably and the specific heat of glass is 840 J/kg · ◦ C. Answer in units of J.

The cup absorbs 18757.2J of heat.

Explanation:

The formula that relates the absorbed or emitted heat with the change in temperature is the following:

Where Q is the heat (or thermal energy), m is the mass of the object, c is its specific heat and ΔT is the change in temperature of the object.

Since the mass of the cup is given in grams, we have to convert it to kilograms:

Now, we can plug all the given values in the formula to obtain the absorbed heat:

It means that the cup absorbed 18757.2J of heat.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.