Question

a. perform calculations using: $(q = mcdot ccdotdelta t)$

1. gold has a specific heat of $0.129j/(g\times^{circ}c)$. how many joules of heat energy are required to raise the temperature of 15 grams of gold from $22^{circ}c$ to 85 $^{circ}c$?

b. determine if its endothermic or exothermic

1. an unknown substance with a mass of 100 grams absorbs 1000 j while undergoing a temperature increase of $15^{circ}c$. what is the specific heat of the substance?

Explanation:

Step1: Calculate heat energy for gold

Given \(m = 15\) g, \(c=0.129\) J/(g·°C), \(\Delta T=T_{final}-T_{initial}=85 - 22=63\) °C.
Using \(q = m\cdot c\cdot\Delta T\), we substitute the values:
\(q=15\times0.129\times63\)
\(q = 15\times8.127\)
\(q=121.905\) J

Step2: Calculate specific heat of unknown substance

Given \(q = 1000\) J, \(m = 100\) g, \(\Delta T = 15\) °C.
From \(q=m\cdot c\cdot\Delta T\), we solve for \(c\):
\(c=\frac{q}{m\cdot\Delta T}\)
Substitute \(q = 1000\), \(m = 100\), \(\Delta T=15\)
\(c=\frac{1000}{100\times15}=\frac{1000}{1500}=\frac{2}{3}\approx0.67\) J/(g·°C)

Answer:

1. The heat energy required for gold is \(121.905\) J.
2. The specific heat of the unknown substance is approximately \(0.67\) J/(g·°C).