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Chapter 21, Problem 30P

(a)

To determine

The efficiency of the battery as an energy storage device.

(a)

Expert Solution
Check Mark

Answer to Problem 30P

The efficiency of the battery as an energy storage device is 0.530_.

Explanation of Solution

Write the expression for the energy taken by the battery.

    Ein=PinΔtin        (I)

Here, Ein is the energy taken by the battery, Pin is the input power, Δtin is the input time interval.

Write the expression for the energy used.

    Eout=PoutΔtout        (II)

Here, Eout is the output energy, Pout is the output power, Δtout is the output time interval.

Write the expression for power.

    P=(ΔV)I        (III)

Here, ΔV is the voltage, I is the current.

Use equation (III) in (II) to solve for Eout.

    Eout=(ΔV)outIout(Δt)out        (IV)

Use equation (III) in (I) to solve for Ein.

    Ein=(ΔV)inIin(Δt)in        (V)

Write the expression for the efficiency.

    efficiency=EoutEin        (VI)

Use 1V=1J/C  and 1A=1C/s relations to solve the equations.

Conclusion:

Substitute 2.3V for ΔVin, 13.5mA for Iin, 4.2h for Δtin in equation (V) to find Ein.

    Ein=(2.3V)(13.5mA×103A1mA)(4.2h×3600s1h)=(2.3J/C)(13.5mC/s×103C/s1C/s)(4.2h×3600s1h)=469J

Substitute 1.6V for ΔVout, 18mA for Iout, 2.4h for Δtout in equation (IV) to find Eout.

    Eout=(1.6V)(18mA×103A1mA)(2.4h×3600s1h)=(1.6J/C)(18mC/s×103C/s1C/s)(2.4h×3600s1h)=249J

Substitute 249J for Eout, 469J for Ein in equation (VI) to find efficiency.

    efficiency=249J469J=0.530

Therefore, the efficiency of the battery as an energy storage device is 0.530_.

(b)

To determine

The internal energy produced in the battery during one charge-discharge cycle.

(b)

Expert Solution
Check Mark

Answer to Problem 30P

The internal energy produced in the battery during one charge-discharge cycle is 221J_.

Explanation of Solution

Write the expression for the Eout.

    Eout=Ein+ΔEint        (VII)

Here, ΔEint is the internal energy produced in the battery during one charge-discharge cycle.

Use equation (VII) to solve for ΔEint.

    ΔEint=EoutEin        (VIII)

Conclusion:

Substitute 249J for Eout, 469J for Ein in equation (VIII) to find ΔEint.

    ΔEint=469J249J=221J

Therefore, the internal energy produced in the battery during one charge-discharge cycle is 221J_.

(c)

To determine

The temperature rise during the cycle of charging and discharging.

(c)

Expert Solution
Check Mark

Answer to Problem 30P

The temperature rise during the cycle of charging and discharging is 15.1°C_.

Explanation of Solution

Write the expression for the heat energy.

    Q=mcΔT        (IX)

Here, Q is the heat energy, m is the mass of the battery, c is the specific heat, ΔT is the temperature rise.

Use equation (IX) to solve for ΔT.

    ΔT=Qmc        (X)

The internal energy ΔEint is used as the heat energy and equation (X) becomes,

    ΔT=ΔEintmc        (XI)

Conclusion:

Substitute 221J for ΔEint, 15.0g for m, 975J/kg°C for c in equation (XI) to find ΔT.

    ΔT=221J(15.0g×103kg1g)(9975J/kg°C)=15.1°C

Therefore, the temperature rise during the cycle of charging and discharging is 15.1°C_.

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Chapter 21 Solutions

Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term

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