The discharge of a firearm can be viewed as then conversion of chemical energy (

Question

The discharge of a firearm can be viewed as then conversion of chemical energy (potential energy) in the propellant into kinetic energy of a bullet. The work (PV work) is done by the hot expanding gases. The conversion is never 100% efficient and energy is lost to the surroundings as friction (bullet moving in the barrel), light (muzzle flash), and heat absorbed by the metal in the gun. For the following problems, assume that the total chemical energy stored in the propellant in ammunition is 6500J; the bullet weighs 6.35g, and the barrel is made of steel with a heat capacity of 0.45 J/(g °C). Kinetic energy is expressed as 1/2mV2 and one J = 1 (kg m2)/s2. ___________a) If the conversion of chemical energy to kinetic energy is 30% efficient, estimate the velocity of the bullet in meters/second. ____________b) If the barrel weighs 18.2g and 10% of the chemical energy is lost to heating the barrel, what will be the final temperature of the barrel? Assume that it starts at room temperature, 25°C. The discharge of a firearm can be viewed as then conversion of chemical energy (potential energy) in the propellant into kinetic energy of a bullet. The work (PV work) is done by the hot expanding gases. The conversion is never 100% efficient and energy is lost to the surroundings as friction (bullet moving in the barrel), light (muzzle flash), and heat absorbed by the metal in the gun. For the following problems, assume that the total chemical energy stored in the propellant in ammunition is 6500J; the bullet weighs 6.35g, and the barrel is made of steel with a heat capacity of 0.45 J/(g °C). Kinetic energy is expressed as 1/2mV2 and one J = 1 (kg m2)/s2. ___________a) If the conversion of chemical energy to kinetic energy is 30% efficient, estimate the velocity of the bullet in meters/second. ____________b) If the barrel weighs 18.2g and 10% of the chemical energy is lost to heating the barrel, what will be the final temperature of the barrel? Assume that it starts at room temperature, 25°C. The discharge of a firearm can be viewed as then conversion of chemical energy (potential energy) in the propellant into kinetic energy of a bullet. The work (PV work) is done by the hot expanding gases. The conversion is never 100% efficient and energy is lost to the surroundings as friction (bullet moving in the barrel), light (muzzle flash), and heat absorbed by the metal in the gun. For the following problems, assume that the total chemical energy stored in the propellant in ammunition is 6500J; the bullet weighs 6.35g, and the barrel is made of steel with a heat capacity of 0.45 J/(g °C). Kinetic energy is expressed as 1/2mV2 and one J = 1 (kg m2)/s2. ___________a) If the conversion of chemical energy to kinetic energy is 30% efficient, estimate the velocity of the bullet in meters/second. ____________b) If the barrel weighs 18.2g and 10% of the chemical energy is lost to heating the barrel, what will be the final temperature of the barrel? Assume that it starts at room temperature, 25°C. The discharge of a firearm can be viewed as then conversion of chemical energy (potential energy) in the propellant into kinetic energy of a bullet. The work (PV work) is done by the hot expanding gases. The conversion is never 100% efficient and energy is lost to the surroundings as friction (bullet moving in the barrel), light (muzzle flash), and heat absorbed by the metal in the gun. For the following problems, assume that the total chemical energy stored in the propellant in ammunition is 6500J; the bullet weighs 6.35g, and the barrel is made of steel with a heat capacity of 0.45 J/(g °C). Kinetic energy is expressed as 1/2mV2 and one J = 1 (kg m2)/s2. ___________a) If the conversion of chemical energy to kinetic energy is 30% efficient, estimate the velocity of the bullet in meters/second. ____________b) If the barrel weighs 18.2g and 10% of the chemical energy is lost to heating the barrel, what will be the final temperature of the barrel? Assume that it starts at room temperature, 25°C.

Explanation / Answer

(a)

Total chemical energy = 6500 J

Conversion to kinetic energy is 30%

Chemical Energy converted to kinetic energy = 0.30 x 6500 J == 1950 J

Now,

velocity can be calculated using following equation:

1/2mV2 =  1950 J

1/2 x 0.00635g x V2 = 1950 J

V= 783.7 m/s

(b)

Energy taken by barrel = 0.10 x 6500J = 650 J

We know ,

m xC x(T2-T1) = 650 J

18.2 g x 0.45 J/(g °C) x ( T - 25 ) =  650 J

T = 104.4 oC

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