Specific Heat Capacity & Transformers: Physics Problems Solved
Hey guys! Today, we're diving into some interesting physics problems. We'll tackle a question about calculating the specific heat capacity of a metal and identifying it, and then we'll explore the function of a transformer. So, let's get started and make physics a little less intimidating, shall we?
898. Calculating Specific Heat Capacity and Identifying the Metal
Let's break down this problem step by step. The core concept here is specific heat capacity, which is the amount of heat energy required to raise the temperature of 1 kilogram of a substance by 1 degree Celsius (or 1 Kelvin). We're given the following information:
- Mass of the substance (m) = 4.5 kg
- Initial temperature (T₁) = 20 °C
- Final temperature (T₂) = 45 °C
- Heat energy supplied (Q) = 14,625 J
Our goal is to find the specific heat capacity (c) and then identify the metal based on that value. The formula we'll use is:
Q = mcΔT
Where:
- Q is the heat energy
- m is the mass
- c is the specific heat capacity
- ΔT is the change in temperature (T₂ - T₁)
First, let's calculate the change in temperature:
ΔT = T₂ - T₁ = 45 °C - 20 °C = 25 °C
Now, we can plug the values into the formula and solve for c:
14,625 J = 4.5 kg * c * 25 °C
To isolate c, we'll divide both sides of the equation by (4.5 kg * 25 °C):
c = 14,625 J / (4.5 kg * 25 °C) c = 14,625 J / 112.5 kg·°C c ≈ 130 J/(kg·°C)
So, the specific heat capacity of the metal is approximately 130 J/(kg·°C). Now, to identify the metal, we need to compare this value to a table of specific heat capacities for different metals. Common metals and their approximate specific heat capacities include:
- Aluminum: ~900 J/(kg·°C)
- Copper: ~385 J/(kg·°C)
- Iron: ~450 J/(kg·°C)
- Lead: ~130 J/(kg·°C)
Comparing our calculated value (130 J/(kg·°C)) to the table, it seems likely that the metal is lead. Lead has a specific heat capacity very close to our calculated value. Remember, this is an approximation, and slight variations can occur due to impurities or other factors, but lead is the most probable answer here.
This problem highlights the relationship between heat energy, mass, specific heat capacity, and temperature change. Understanding this relationship is crucial for various applications, from engineering design to material science. Guys, make sure you understand the formula Q = mcΔT and how to manipulate it to solve for different variables. This is a fundamental concept in thermodynamics!
899. Understanding Transformers
Now, let's shift gears and talk about transformers. A transformer is a crucial device in electrical systems, and its primary function is to change the voltage of alternating current (AC). It's important to emphasize that transformers only work with AC, not direct current (DC). Why is this important, you ask? Well, the magic behind a transformer relies on the principle of electromagnetic induction, which requires a changing magnetic field, something that AC naturally provides due to its alternating nature.
Think about it this way: AC voltage and current are constantly changing direction and magnitude, which creates a fluctuating magnetic field. This fluctuating field is what drives the transformer's operation. DC, on the other hand, provides a steady, unchanging current, resulting in a static magnetic field that cannot induce a voltage change in the transformer's secondary coil. So, remember, transformers are AC devices through and through!
So, how exactly does a transformer work its voltage-changing magic? At its core, a transformer consists of two or more coils of wire, called windings, that are electrically isolated but magnetically linked. These windings are typically wound around a common iron core, which helps to concentrate the magnetic field. We have a primary winding, which is connected to the input AC voltage, and a secondary winding, which provides the output voltage.
The beauty of a transformer lies in the relationship between the number of turns in the primary and secondary windings. This ratio directly determines the voltage transformation. If the secondary winding has more turns than the primary winding, the transformer will step up the voltage (increase it). Conversely, if the secondary winding has fewer turns than the primary winding, the transformer will step down the voltage (decrease it). The ratio of the number of turns in the secondary winding (Nₛ) to the number of turns in the primary winding (Nₚ) is called the turns ratio, and it's a key factor in determining the voltage transformation. The relationship can be expressed as:
Vₛ / Vₚ = Nₛ / Nₚ
Where:
- Vₛ is the voltage in the secondary winding
- Vₚ is the voltage in the primary winding
- Nₛ is the number of turns in the secondary winding
- Nₚ is the number of turns in the primary winding
For example, if a transformer has a primary winding with 100 turns and a secondary winding with 200 turns (a turns ratio of 2:1), and the input voltage is 120 V, the output voltage will be 240 V (assuming ideal conditions with no losses). This step-up functionality is crucial in power transmission, where high voltages are used to minimize current and reduce energy loss over long distances. Conversely, step-down transformers are used to reduce the high transmission voltages to safer levels for use in homes and businesses.
The applications of transformers are vast and pervasive in our modern world. They are integral to the efficient transmission and distribution of electrical power, playing a vital role in the electrical grid that powers our homes and industries. Power plants generate electricity at relatively low voltages, but stepping up the voltage for long-distance transmission is crucial to minimize energy loss due to the resistance of the wires. This is where step-up transformers come into play, boosting the voltage to hundreds of thousands of volts for efficient transmission.
Once the electricity reaches urban areas or industrial facilities, it needs to be stepped down to usable levels. This is achieved through a series of step-down transformers, strategically located in substations and distribution networks, that gradually reduce the voltage to safer levels for residential and commercial use. The voltage is typically stepped down to a few thousand volts at substations and then further reduced to 120 V or 240 V for use in homes and businesses. This multi-stage transformation process ensures that electricity is delivered safely and efficiently to consumers.
Beyond the power grid, transformers are also essential components in a wide range of electronic devices and appliances. You'll find them in everything from your smartphone charger and laptop power adapter to microwave ovens, televisions, and audio amplifiers. In these applications, transformers are used to convert the AC voltage from the wall outlet to the specific voltage required by the device's internal circuitry. For instance, a laptop power adapter uses a transformer to step down the 120 V AC from the outlet to a lower DC voltage (typically around 19 V) that the laptop can use.
Furthermore, transformers are indispensable in industrial applications, such as powering heavy machinery, welding equipment, and industrial control systems. They are also used in medical equipment, such as MRI machines and X-ray machines, where precise voltage and current control are essential. The versatility and reliability of transformers have made them a cornerstone of modern technology, enabling the efficient and safe use of electricity in countless applications.
In summary, guys, transformers are fundamental devices that allow us to efficiently and safely manage electrical power. Their ability to step up or step down voltage makes them indispensable in power transmission, distribution, and countless electronic applications. Understanding the principles behind transformer operation is crucial for anyone working with electrical systems or electronics. Remember the turns ratio and how it affects voltage transformation, and you'll have a solid grasp of this essential technology!