Question

1. which sample is most likely to undergo the largest change in temperature upon the absorption of 100 kj of heat? a. 10 g water b. 10 g iron c. 100 g water d. 100 g iron e. same δt

Explanation:

Step1: Recall the heat - capacity formula

The formula for heat \(q = mc\Delta T\), where \(q\) is the heat absorbed or released, \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the change in temperature. We can solve for \(\Delta T=\frac{q}{mc}\). The specific heat capacity of water \(c_{water}=4.184\space J/(g\cdot^{\circ}C)\) and the specific heat capacity of iron \(c_{iron} = 0.45\space J/(g\cdot^{\circ}C)\)

Step2: Calculate \(\Delta T\) for each option

• Option A (\(m = 10\space g\), \(c = 4.184\space J/(g\cdot^{\circ}C)\), \(q=100\times10^{3}\space J\))

\(\Delta T=\frac{q}{mc}=\frac{100\times 10^{3}\space J}{10\space g\times4.184\space J/(g\cdot^{\circ}C)}\approx2390^{\circ}C\)

• Option B (\(m = 10\space g\), \(c = 0.45\space J/(g\cdot^{\circ}C)\), \(q = 100\times10^{3}\space J\))

\(\Delta T=\frac{q}{mc}=\frac{100\times 10^{3}\space J}{10\space g\times0.45\space J/(g\cdot^{\circ}C)}\approx22222^{\circ}C\)

• Option C (\(m = 100\space g\), \(c = 4.184\space J/(g\cdot^{\circ}C)\), \(q=100\times10^{3}\space J\))

\(\Delta T=\frac{q}{mc}=\frac{100\times 10^{3}\space J}{100\space g\times4.184\space J/(g\cdot^{\circ}C)}\approx239^{\circ}C\)

• Option D (\(m = 100\space g\), \(c = 0.45\space J/(g\cdot^{\circ}C)\), \(q = 100\times10^{3}\space J\))

\(\Delta T=\frac{q}{mc}=\frac{100\times 10^{3}\space J}{100\space g\times0.45\space J/(g\cdot^{\circ}C)}\approx2222^{\circ}C\)

Answer:

B. 10 g iron